CIRCLE SYSTEM-03-(ASSIGNMENT) PART-I

1. The two points A and B in a plane such that for all points P lies on circle satisfied then k will not be equal to (a) 0 (b) 1 (c) 2 (d) None of these 2. Locus of a point which moves such that sum of the squares of its distances from the sides of a square of side unity is 9, is (a) Straight line (b) Circle (c) Parabola (d) None of these 3. The equation of the circle which touches both the axes and whose radius is a, is (a) (b) (c) (d) 4. ABCD is a square the length of whose side is a. Taking AB and AD as the coordinate axes, the equation of the circle passing through the vertices of the square, is (a) (b) (c) (d) 5. The equation of the circle in the first quadrant touching each coordinate axis at a distance of one unit from the origin is (a) (b) (c) (d) None of these 6. The equation of the circle which touches both axes and whose centre is , is (a) (b) (c) (d) 7. The equation of the circle which touches x-axis and whose centre is (1, 2), is (a) (b) (c) (d) 8. The equation of the circle having centre (1, – 2) and passing through the point of intersection of lines is (a) (b) (c) (d) 9. The equation of the circle passing through (4, 5) and having the centre at (2, 2), is (a) (b) (c) (d) 10. The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line is (a) (b) (c) (d) 11. The equation of the circle passing through the points (0, 0), (0, b) and (a, b) is (a) (b) (c) (d) 12. The equation will represent a circle, if (a) a = b = 0 and c = 0 (b) f = g and h = 0 (c) a = b  0 and h = 0 (d) f = g and c = 0 13. The equation of the circle whose diameters have the end points (a, 0), (0, b) is given by (a) (b) (c) (d) 14. The equation of the circle which touches x-axis at (3, 0) and passes through (1, 4) is given by (a) (b) (c) (d) 15. From three non-collinear points we can draw (a) Only one circle (b) Three circle (c) Infinite circles (d) No circle 16. Equation of a circle whose centre is origin and radius is equal to the distance between the lines x = 1 and x = – 1 is (a) (b) (c) (d) 17. If the centre of a circle is (2, 3) and a tangent is then the equation of this circle is (a) (b) (c) (d) 18. represents a circle through the origin, if (a) a = 0, b = 0, c = 2 (b) a = 1, b = 0, c = 0 (c) a = 2, b = 2, c = 0 (d) a = 2, b = 0, c = 0 19. If the equation represents a circle, then K = (a) 3/4 (b) 1 (c) 4/3 (d) 12 20. A circle has radius 3 units and its centre lies on the line Then the equation of this circle if it passes through point (7, 3), is (a) (b) (c) (d) None of these 21. The equation of circle whose diameter is the line joining the points (– 4, 3) and (12, –1) is (a) (b) (c) (d) 22. The equation of the circle which passes through the points (3, – 2) and (– 2, 0) and centre lies on the line is (a) (b) (c) (d) None of these 23. For to represent a circle, one must have (a) a = 3, h = 0 (b) a = 1, h = 0 (c) a = h = 3 (d) a = h = 0 24. The equation of the circle in the first quadrant which touches each axis at a distance 5 from the origin is (a) (b) (c) (d) 25. If is the centre of a circle passing through the origin, then its equation is (a) (b) (c) (d) 26. The equation of the circle whose diameter lies on and and which passes through (4, 6) is (a) (b) (c) (d) 27. The equation of the circle of radius 5 and touching the coordinate axes in third quadrant is (a) (b) (c) (d) 28. The centre of a circle is (2, – 3) and the circumference is 10. Then the equation of the circle is (a) (b) (c) (d) 29. The circle described on the line joining the points (0, 1), (a, b) as diameter cuts the x-axis in points whose abscissae are roots of the equation (a) (b) (c) (d) . 30. Four distinct points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle for (a) All integral values of k (b) 0 < k < 1 (c) k < 0 (d) For two values of k 31. The equations of the circles which touch both the axes and the line x = a are (a) (b) (c) (d) None of these. 32. The equation of the unit circle concentric with is (a) (b) (c) (d) 33. A circle of radius 2 touches the coordinate axes in the first quadrant. If the circle makes a complete rotation on the x-axis along the positive direction of the x-axis then the equation of the circle in the new position is (a) (b) (c) (d) None of these 34. A circle which touches the axes and whose centre is at distance from the origin, has the equation (a) (b) (c) (d) None of these 35. If (– 1, 4) and (3, – 2) are end points of a diameter of a circle, then the equation of this circle is (a) (b) (c) (d) 36. The equation of the circle concentric with the circle and passing through the point (– 1, – 2) is (a) (b) (c) (d) None of these 37. If (– 3, 2) lies on the circle which is concentric with then c is equal to (a) – 11 (b) 11 (c) – 24 (d) 24 38. Equation represents (a) A circle (b) A pair of two different lines (c) A pair of coincident lines (d) A point 39. If the lines and lie along diameters of a circle of circumference 10, then the equation of the circle is (a) (b) (c) (d) 40. is a chord of a circle of radius a and the diameter of the circle lies along x-axis and one end of this chord is origin. The equation of the circle described on this chord as diameter is (a) (b) (c) (d) 41. If is a chord of the circle then the equation of the circle of which this chord is a diameter, is (a) (b) (c) (d) 42. The circle on the chord of the circle as diameter has the equation (a) (b) (c) (d) 43. The equation of circle which touches the axes of coordinates and the line and whose centre lies in the first quadrant is where c is (a) 1 (b) 2 (c) 3 (d) 6 44. The equation of a circle which touches both axes and the line and lies in the third quadrant is (a) (b) (c) (d) 45. Equation of the circle which touches the lines and is (a) (b) (c) (d) 46. The equation of the circumcircle of the triangle formed by the lines and y = 0, is (a) (b) (c) (d) 47. A variable circle passes through the fixed point and touches x-axis. The locus of the other end of the diameter through A is (a) (b) (c) (d) 48. If a circle passes through the points of intersection of the coordinate axes with the lines and then the value of  is (a) 1 (b) 2 (c) 3 (d) 4 49. Equation to the circles which touch the lines and pass through (2, 3) are (a) (b) (c) Both (a) and (b) (d) None of these 50. The equation of the circle which passes through (1, 0) and (0, 1) and has its radius as small as possible, is (a) (b) (c) (d) 51. The centres of a set of circles, each of radius 3, lie on the circle The locus of any point in the set is (a) (b) (c) (d) 52. The equation of the circle which touches both the axes and the straight line in the first quadrant and lies below it is (a) (b) (c) (d) 53. Three sides of a triangle have the equations Then where is the equation of the circumcircle of the triangle, if (a) (b) (c) Both (a) and (b) hold together (d) None of these 54. The equation of the circle passing through the point (1, 1) and having two diameters along the pair of lines is (a) (b) (c) (d) None of these 55. The equation of a circle which touches x-axis and the line its centre lying in the third quadrant and lies on the line is (a) (b) (c) (d) None of these 56. Two vertices of an equilateral triangle are (– 1, 0) and (1, 0) and its third vertex lies above the x-axis. The equation of the circumcircle of the triangle is (a) (b) (c) (d) None of these 57. A triangle is formed by the lines whose combined equation is given by The equation of its circumcircle is (a) (b) (c) (d) None of these 58. If the centroid of an equilateral triangle is (1, 1) and its one vertex is (– 1, 2) then the equation of its circumcircle is (a) (b) (c) (d) None of these 59. The equation of the circle whose one diameter is PQ, where the ordinates of P, Q are the roots of the equation and the abscissae are the roots of the equation is (a) (b) (c) (d) None of these 60. The equation of the circumcircle of an equilateral triangle is and one vertex of the triangle is (1, 1). The equation of incircle of the triangle is (a) (b) (c) (d) None of these 61. The equation of the circle of radius whose centre lies on the line and which touches the line , and whose centre's coordinates satisfy the inequality is (a) (b) (c) (d) None of these 62. The circumcircle of the quadrilateral formed by the lines is (a) (b) (c) (d) 63. Equation of a circle , which touches the line at (1, 1) is given by (a) (b) (c) (d) None of these 64. The area of the circle whose centre is at (1, 2) and which passes through the point (4, 6) is (a) 5 (b) 10 (c) 25 (d) None of these 65. The centres of the circles and are (a) Same (b) Collinear (c) Non-collinear (d) None of these 66. If a circle passes through the point (0, 0), (a, 0), (0, b), then its centre is (a) (a, b) (b) (b, a) (c) (d) 67. If the radius of the circle be 11, then k = (a) 347 (b) 4 (c) – 4 (d) 49 68. The centre and radius of the circle are (a) and (b) and (c) and (d) and 69. Centre of the circle is (a) (3, 4) (b) (– 3, – 4) (c) (4, 3) (d) (– 4, – 3) 70. A circle has its equation in the form Choose the correct coordinates of its centre and the right value of its radius from the following (a) Centre (– 1, –2), radius = 2 (b) Centre (2, 1), radius = 1 (c) Centre (1, 2), radius = 3 (d) Centre (– 1, 2), radius = 2 71. A circle touches the axes at the points (3, 0) and (0, – 3). The centre of the circle is (a) (3, – 3) (b) (0, 0) (c) (– 3, 0) (d) (6, – 6) 72. Radius of the circle is (a) 1 (b) 3 (c) (d) 73. The area of a circle whose centre is (h, k) and radius a is (a) (b) (c) (d) None of these 74. If the coordinates of one end of the diameter of the circle are (– 3, 2), then the coordinates of other end are (a) (5, 3) (b) (6, 2) (c) (1, – 8) (d) (11, 2) 75. The centre of the circle is (a) (1, – 3) (b) (– 1, 3) (c) (1, 3) (d) None of these 76. If then the equation will represent (a) A circle of radius g (b) A circle of radius f (c) A circle of diameter (d) A circle of radius 0 77. The centre of circle inscribed in square formed by the lines and is (a) (4, 7) (b) (7, 4) (c) (9, 4) (d) (4, 9) 78. The equation will represent a real circle if (a) (b) (c) Always (d) None of these 79. One of the diameters of the circle is given by (a) (b) (c) (d) 80. The radius of the circle passing through the point (6, 2) two of whose diameters are and is (a) 10 (b) (c) 6 (d) 4 81. If the equation of a circle is then its centre is (a) (2, 0) (b) (2/3, 0) (c) (– 2/3, 0) (d) None of these 82. If represents a circle of meaningful radius then the range of real values of is (a) R (b) (c) (d) None of these 83. The locus of the centres of the circles for which one end of a diameter is (1, 1) while the other end is on the line is (a) (b) (c) (d) None of these 84. If A and B are two points on the circle which are farthest and nearest respectively from the point (7, 2) then (a) (b) (c) (d) 85. The radius of the circle passing through the point (5, 4) and concentric to the circle is (a) 5 (b) (c) 10 (d) 86. The length of the radius of the circle is (a) (b) (c) (d) 87. is the centre of a circle. If (x, 3) and (3, 5) are end points of a diameter of this circle, then (a) (b) (c) (d) None of these 88. The greatest distance of the point P (10, 7) from the circle is (a) 5 (b) 15 (c) 10 (d) None of these 89. If one end of a diameter of the circle be (3, 4), then the other end is (a) (0, 0) (b) (1, 1) (c) (1, 2) (d) (2, 1) 90. If and are the tangents of same circle, then its radius will be (a) (b) (c) (d) 91. If and are two tangents to a circle, then the radius of the circle is (a) 1 (b) 2 (c) 4 (d) 6 92. If is the equation of a circle then its radius is (a) (b) (c) (d) None of these 93. C1 is a circle of radius 1 touching the x-axis and the y-axis. C2 is another circle of radius >1 and touching the axes as well as the circle C1. Then the radius of C2 is (a) (b) (c) (d) None of these 94. If p and q be the longest distance and the shortest distance respectively of the point (– 7, 2) from any point (, ) on the curve whose equation is then GM of p and q is equal to (a) (b) (c) 13 (d) None of these 95. The equation of a circle is The centre of the smallest circle touching this circle and the line has the coordinates (a) (b) (c) (d) None of these 96. A circle touches the line at the point (3, 5). If its centre lies on the line then the centre of that circle is (a) (3, 2) (b) (– 3, 8) (c) (4, 1) (d) (8, – 3) 97. The locus of the centre of the circle is (a) (b) (c) (d) 98. If a circle touches at the point (2, 3) of the line and then radius of such circle (a) 2 units (b) 4 units (c) units (d) units 99. A circle touches the y-axis at the point (0, 4) and cuts the x-axis in a chord of length 6 units. The radius of the circle is (a) 3 (b) 4 (c) 5 (d) 6 100. The radius of a circle which touches y-axis at (0, 3) and cuts intercept of 8 units with x-axis, is (a) 3 (b) 2 (c) 5 (d) 8 101. The intercept on the line by the circle is AB. Equation of the circle with AB as a diameter is (a) (b) (c) (d) 102. The circle cuts x-axis at (a) (2, 0), (– 3, 0) (b) (3, 0), (4, 0) (c) (1, 0), (– 1, 0) (d) (1, 0), (2, 0) 103. If the line meets the circle at A and B, then the equation of the circle having AB as a diameter will be (a) (b) (c) (d) None of these 104. If the circle touches x-axis, then the value of a is (a) 16 (b) 4 (c) 8 (d) 1 105. The length of the intercept made by the circle on the line is (a) 2 (b) (c) (d) 106. The AM of the abscissae of points of intersection of the circle with x-axis is (a) g (b) – g (c) f (d) – f 107. The straight line cuts the circle at (a) No points (b) One point (c) Two points (d) None of these 108. The equation of a circle whose centre is (3, – 1) and which cuts off a chord of length 6 on the line (a) (b) (c) (d) None of these 109. The points of intersection of the line and the circle are (a) (– 2, – 6), (4, 2) (b) (2, 6), (– 4, – 2) (c) (– 2, 6), (– 4, 2) (d) None of these 110. The line intersects the circle at two real distinct points, if (a) (b) (c) (a) and (b) both (d) 111. A line through (0, 0) cuts the circle at A and B, then locus of the centre of the circle drawn AB as diameter is (a) (b) (c) (d) 112. If the line cuts the circle at two real points then the number of possible values of m is (a) 1 (b) 2 (c) Infinite (d) None of these 113. The GM of the abscissae of the points of intersection of the circle and the line y = 1 is (a) (b) (c) (d) 1 114. The equation(s) of the tangent at the point (0, 0) to the circle, making intercepts of length 2a and 2b units on the coordinate axes, is (are) (a) (b) (c) (d) None of these 115. A circle which passes through origin and cuts intercepts on axes a and b, the equation of circle is (a) (b) (c) (d) 116. Let L1 be a straight line passing through the origin and L2 be the straight line If the intercepts made by the circle on L1 and L2 are equal, then which of the following equations can represent L1 (a) (b) (c) (d) 117. The two lines through (2, 3) from which the circle intercepts chords of length 8 units have equations (a) (b) (c) (d) None of these 118. Circles are drawn through the point (2, 0) to cut intercepts of length 5 units on the x-axis. If their centres lie in the first quadrant, then their equation is (a) (b) (c) (d) 119. A circle touches the y-axis at (0, 2) and has an intercept of 4 units on the positive side of the x-axis. Then the equation of the circle is (a) (b) (c) (d) None of these 120. Circles are drawn through the point (3, 0) to cut an intercept of length 6 units on the negative direction of the x-axis. The equation of the locus of their centres is (a) The x-axis (b) (c) The y-axis (d) 121. Circles and cut off equal intercepts on a line through the point . The slope of the line is (a) (b) (c) (d) None of these 122. If 2l be the length of the intercept made by the circle on the line then is equal to (a) (b) (c) (d) 123. For the circle the following statement is true (a) The length of tangent from (1, 2) is 7 (b) Intercept on y-axis is 2 (c) Intercept on x-axis is (d) None of these 124. The length of the chord joining the points in which the straight line cuts the circle is (a) 1 (b) 2 (c) 4 (d) 8 125. A line is drawn through a fixed point P (, ) to cut the circle at A and B. Then PA . PB is equal to (a) (b) (c) (d) None of these 126. The range of values of m for which the line cuts the circle at distinct or coincident points is (a) (b) (c) (d) None of these 127. A point inside the circle is (a) (– 1, 3) (b) (– 2, 1) (c) (2, 1) (d) (–3, 2) 128. Position of the point (1, 1) with respect to the circle is (a) Outside the circle (b) Upon the circle (c) Inside the circle (d) None of these 129. The number of tangents that can be drawn from (0, 0) to the circle is (a) None (b) One (c) Two (d) Infinite 130. The number of tangents which can be drawn from the point (– 1, 2) to the circle is (a) 1 (b) 2 (c) 3 (d) 0 131. The point (0.1, 3.1) with respect to the circle , is (a) At the centre of the circle (b) Inside the circle but not at the centre (c) On the circle (d) Outside the circle 132. The number of the tangents that can be drawn from (1, 2) to is (a) 1 (b) 2 (c) 3 (d) 0 133. The number of points on the circle which are at a distance 2 from the point (– 2, 1) is (a) 2 (b) 0 (c) 1 (d) None of these 134. If is a given circle and (0, 0), (1, 8) are two points, then (a) Both the points are inside the circle (b) Both the points are outside the circle (c) One point is on the circle another is outside the circle (d) One point is inside and another is outside the circle 135. A region in the x-y plane is bounded by the curve and the line y = 0. If the point lies in the interior of the region, then (a) (b) (c) (d) None of these 136. If (2, 4) is a point interior to the circle and the circle does not cut the axes at any point , then  belongs to the interval (a) (25, 32) (b) (9, 32) (c) (32, +) (d) None of these 137. The range of values of for which is an interior point of the circle is (a) (b) (c) (d) 138. The range of values of r for which the point is an interior point of the major segment of the circle cut off by the line is (a) (b) (c) (d) None of these 139. If P (2, 8) is an interior point of a circle which neither touches nor intersects the axes, then set for p is (a) p < – 1 (b) p < – 4 (c) p > 96 (d)  140. The equation of the tangent to the circle at (a, b) is where  is (a) (b) (c) (d) None of these 141. touches the circle then the coordinates of the point of contact are (a) (7, 3) (b) (7, 4) (c) (7, 8) (d) (7, 2) 142. A circle with centre (a, b) passes through the origin. The equation of the tangent to the circle at the origin is (a) (b) (c) (d) 143. If the tangent at a point of a curve is perpendicular to the line that joins origin with the point P, then the curve is (a) Circle (b) Parabola (c) Ellipse (d) Straight line 144. The circle touches (a) x-axis only (b) y-axis only (c) Both x and y-axis (d) Does not touch any axis 145. The condition that the line may touch the circle is (a) (b) (c) (d) 146. The equation of circle with centre (1, 2) and tangent is (a) (b) (c) (d) 147. The equation of tangent to the circle parallel to is (a) (b) (c) (d) None of these 148. The line meets the circle at only one point, if (a) (b) (c) (d) 149. The line will be a tangent to the circle if (a) (b) (c) (d) 150. The circle touches (a) x-axis (b) y-axis (c) x-axis and y-axis (d) None of these 151. If the line be a tangent to the circle then the locus of the point (l, m) is (a) A straight line (b) A circle (c) A parabola (d) An ellipse 152. The straight line touches the circle at the point whose coordinates are (a) (1, – 2) (b) (1, 2) (c) (– 1, 2) (d) (– 1, – 2) 153. If the straight line touches the circle then the value of c will be (a) (b) (c) (d) 154. At which point on y-axis the line x = 0 is a tangent to circle (a) (0, 1) (b) (0, 2) (c) (0, 3) (d) (0, 4) 155. At which point the line touches to the circle or Line is a tangent to the circle at (a) (b) (c) (d) 156. If the line touches the circle then the value of r will be (a) 2 (b) 5 (c) (d) 157. If the centre of a circle is (– 6, 8) and it passes through the origin, then equation to its tangent at the origin, is (a) (b) (c) (d) 158. If the line touches the circle then  is equal to (a) – 35, – 15 (b) – 35, 15 (c) 35, 15 (d) 35, – 15 159. The tangent to which is parallel to y-axis and does not lie in the third quadrant touches the circle at the point (a) (3, 0) (b) (– 3, 0) (c) (0, 3) (d) (0, – 3) 160. The points of contact of tangents to the circle which are inclined at an angle of 30o to the x-axis are (a) (b) (c) (d) None of these. 161. If the line touches , then the locus of the point (h, k) is a circle of radius (a) a (b) (c) (d) 162. The slope of the tangent at the point (h, h) of the circle is (a) 0 (b) 1 (c) – 1 (d) Depends on h. 163. The line is a tangent to the circle (a) (b) (c) (d) None of these 164. The point of contact of a tangent from the point (1, 2) to the circle has the coordinates (a) (b) (c) (d) 165. If the line is a tangent to a circle with centre (2, 3), then its equation will be (a) (b) (c) (d) None of these 166. A tangent to the circle meets the axes at points A and B. The locus of the mid point of AB is (a) (b) (c) (d) 167. If the tangent to the circle at point (1, –2) touches the circle then its point of contact is (a) (– 1, – 3) (b) (3, – 1) (c) (– 2, 1) (d) (5, 0) 168. The equation of the tangent to the circle which is inclined at 60o angle with x-axis, will be (a) (b) (c) (d) None of these 169. If is a tangent to the circle then (a) (b) (c) (d) 170. If the circle is a tangent to the curve at a point (1, 2), then the possible location of the points (h, k) are given by (a) (b) (c) (d) 171. If the tangent at the point P on the circle meets the straight line at a point Q on the y-axis, then the length of PQ is (a) 4 (b) (c) 5 (d) 172. The tangents to having inclinations and intersect at P. If cot then the locus of P is (a) (b) (c) (d) None of these 173. If the points A (1, 4) and B are symmetrical about the tangent to the circle at the origin then coordinates of B are (a) (1, 2) (b) (c) (4, 1) (d) None of these 174. A line parallel to the line touches the circle at the point (a) (1, – 4) (b) (1, 2) (c) (3, – 4) (d) (3, 2) 175. The possible values of p for which the line is a tangent to the circle is/are (a) 0 and q (b) q and 2q (c) 0 and 2q (d) q 176. A circle passes through (0, 0) and (1, 0) and touches to the circle then the centre of circle is (a) (b) (c) (d) 177. The length of tangent from the point (5, 1) to the circle is (a) 81 (b) 29 (c) 7 (d) 21 178. Length of the tangent from to the circle is (a) (b) (c) (d) None of these 179. The length of the tangent from the point (4, 5) to the circle is (a) (b) (c) (d) 180. The square of the length of the tangent from (3, – 4) on the circle is (a) 20 (b) 30 (c) 40 (d) 50 181. The length of the tangent from (0, 0) to the circle is (a) (b) (c) (d) 182. The length of the tangent to the circle from (–1, – 3) is (a) 2 (b) (c) 4 (d) 8 183. A tangent is drawn to the circle and it touches the circle at point A. The tangent passes through the point P (2, 1). Then PA is equal to (a) 4 (b) 2 (c) (d) None of these 184. Lines are drawn through the point to meet the circle . The length of the line segment PA, A being the point on the circle where the line meets the circle at coincident points, is (a) 16 (b) (c) 48 (d) None of these 185. The coordinates of the point from where the tangents are drawn to the circles and are of same length, are (a) (b) (c) (d) 186. Length of the tangent drawn from any point on the circle to the circle is (a) (b) (c) (d) None of these 187. If P is a point such that the ratio of the squares of the lengths of the tangents from P to the circles and is 2 : 3, then the locus of P is a circle with centre (a) (7, – 8) (b) (– 7, 8) (c) (7, 8) (d) (– 7, – 8) 188. The lengths of the tangents from any point on the circle to the two circles are in the ratio (a) 1 : 2 (b) 2 : 3 (c) 3 : 4 (d) None of these 189. If the squares of the lengths of the tangents from a point P to the circles and are in A. P., then (a) a, b, c are in G.P. (b) a, b, c are in A.P. (c) are in A.P. (d) are in G.P. 190. A pair of tangents are drawn from the origin to the circle . The equation of the pair of tangents is (a) (b) (c) (d) 191. The equations of the tangents drawn from the origin to the circle are (a) (b) (c) (d) 192. The equations of the tangents drawn from the point (0, 1) to the circle are (a) (b) (c) (d) 193. The two tangents to a circle from an external point are always (a) Equal (b) Perpendicular to each other (c) Parallel to each other (d) None of these 194. The equation of pair of tangents to the circle from (6, – 5), is (a) (b) (c) (d) None of these 195. Tangents drawn from origin to the circle are perpendicular to each other, if (a) (b) (c) (d) 196. The equation to the tangents to the circle which are parallel to are (a) (b) (c) (d) 197. If is a tangent to the circle with centre at the point (2, – 1), then the equation of the other tangent to the circle from the origin is (a) (b) (c) (d) 198. The equation of a tangent to the circle passing through (–2, 11) is (a) (b) (c) (d) 199. Tangents drawn from the point (4, 3) to the circle are inclined at an angle (a) (b) (c) (d) 200. The angle between the pair of tangents from the point (1, 1/2) to the circle is (a) (b) (c) (d) None of these 201. The equation of the pair of tangents drawn from the point (0, 1) to the circle is (a) (b) (c) (d) 202. The angle between the two tangents from the origin to the circle is (a) 0 (b) (c) (d) 203. Tangents are drawn from the point (4, 3) to the circle . The area of the triangle formed by them and the line joining their points of contact is (a) (b) (c) (d) 204. An infinite number of tangents can be drawn from (1, 2) to the circle , then (a) – 20 (b) 0 (c) 5 (d) Cannot be determined 205. The area of the triangle formed by the tangents from the points (h, k) to the circle and the line joining their points of contact is (a) (b) (c) (d) 206. Two tangents PQ and PR drawn to the circle from point P (16, 7). If the centre of the circle is C then the area of quadrilateral PQCR will be (a) 75 sq. units (b) 150 sq. units (c) 15 sq. units (d) None of these 207. The tangents are drawn from the point (4, 5) to the circle The area of quadrilateral formed by these tangents and radii, is (a) 15 sq. units (b) 75 sq. units (c) 8 sq. units (d) 4 sq. units 208. Tangents are drawn to the circle from a point 'P' lying on the x-axis. These tangents meet the y-axis at points 'P1' and 'P2' . Possible coordinates of 'P' so that area of triangle PP1P2 is minimum, is /are (a) (10, 0) (b) (c) (– 10, 0) (d) 209. The angle between the tangents from ,  to the circle is , (where ) (a) (b) (c) (d) None of these 210. The normal to the circle at the point (– 3, 4), is (a) (b) (c) (d) 211. The equation of normal to the circle at (1, 1) is (a) (b) (c) (d) None of these 212. The normal at the point (3, 4) on a circle cuts the circle at the point ( –1, –2). Then the equation of the circle is (a) (b) (c) (d) 213. The line is a normal to the circle if (a) (b) (c) (d) None of these 214. The equation of a normal to the circle passing through (0, 0) is (a) (b) (c) (d) 215. The equation of the normal at the point (4, – 1) of the circle is (a) (b) (c) (d) 216. The equation of the normal to the circle at (0, 0) is (a) (b) (c) (d) 217. The area of triangle formed by the tangent, normal drawn at to the circle and positive x-axis, is (a) (b) (c) (d) None of these 218. is the equation of normal at to which of the following circles (a) (b) (c) (d) 219. The line is normal to the circle . The portion of the line intercepted by this circle is of length (a) r (b) (c) 2r (d) 220. If the straight line touches the circle and is normal to the circle then the values of a and b are respectively (a) 1, – 1 (b) 1, 2 (c) (d) 2, 1 221. The number of feet of normals from the point (7, ¬– 4) to the circle is (a) 1 (b) 2 (c) 3 (d) 4