5.3-HYPERBOLA -02-ASSIGNMENT

1. The locus of the centre of a circle, which touches externally the given two circle, is (a) Circle (b) Parabola (c) Hyperbola (d) Ellipse 2. The locus of a point which moves such that the difference of its distances from two fixed points is always a constant is (a) A straight line (b) A circle (c) An ellipse (d) A hyperbola 3. The one which does not represent a hyperbola is (a) (b) (c) (d) 4. The equation of the hyperbola whose directrix is , focus (2, 1) and eccentricity 2 will be (a) (b) (c) (d) None of these 5. The locus of the point of intersection of the lines and for different value of k is (a) Circle (b) Parabola (c) Hyperbola (d) Ellipse 6. Locus of the point of intersection of straight line and is (a) An ellipse (b) A circle (c) A hyperbola (d) A parabola 7. The eccentricity of the hyperbola is (a) (b) 2 (c) 3 (d) 8. Centre of hyperbola is (a) (1, –1) (b) (–1, 1) (c) (–1, –1) (d) (1, 1) 9. The eccentricity of the conic is (a) (b) (c) (d) 10. The eccentricity of a hyperbola passing through the point (3, 0), will be (a) (b) (c) (d) 11. If (4, 0) and (–4, 0)be the vertices and (6, 0) and (–6, 0) be the foci of a hyperbola, then its eccentricity is (a) 5/2 (b) 2 (c) 3/2 (d) 12. If e and are eccentricities of hyperbola and its conjugate respectively, then (a) (b) (c) (d) 13. If e and are the eccentricities of the ellipse and the hyperbola respectively, then = (a) 9 (b) 4 (c) 5 (d) 1 14. The directrix of the hyperbola is (a) (b) (c) (d) 15. The latus rectum of the hyperbola , is (a) (b) (c) (d) 16. The foci of the hyperbola , is (a) (b) (c) (d) None of these 17. The distance between the directrices of a rectangular hyperbola is 10 units, then distance between its foci is (a) (b) 5 (c) (d) 20 18. The difference of the focal distances of any point on the hyperbola , is (a) 8 (b) 7 (c) 6 (d) 4 19. If the length of the transverse and conjugate axes of a hyperbola be 8 and 6 respectively, then the difference of focal distances of any point of the hyperbola will be (a) 8 (b) 6 (c) 14 (d) 2 20. The length of transverse axis of the hyperbola is (a) (b) (c) (d) 21. A hyperbola passes through the points (3, 2) and (–17, 12) and has its centre at origin and transverse axis is along x-axis. The length of its transverse axis is (a) 2 (b) 4 (c) 6 (d) None of these 22. The equation of the hyperbola whose foci are the foci of the ellipse and the eccentricity is 2, is (a) (b) (c) (d) 23. The distance between the foci of a hyperbola is double the distance between its vertices and the length of its conjugate axis is 6. The equation of the hyperbola referred to its axes as axes of coordinates is (a) (b) (c) (d) 24. If and be the foci and vertices of a hyperbola then its equation is (a) (b) (c) (d) 25. The length of the transverse axis of a hyperbola is 7 and it passes through the point (5, –2), the equation of the hyperbola is (a) (b) (c) (d) None of these 26. If the centre, vertex and focus of a hyperbola be (0, 0),(4, 0) and (6, 0) respectively, then the equation of the hyperbola is (a) (b) (c) (d) 27. The equation of a hyperbola, whose foci are (5, 0) and (–5, 0) and the length of whose conjugate axis is 8, is (a) (b) (c) (d) 28. If the latus rectum of an hyperbola be 8 and eccentricity be , then the equation of the hyperbola is (a) (b) (c) (d) 29. The equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13, is (a) (b) (c) (d) 30. For hyperbola which of the following remains constant with change in (a) Abscissae of vertices (b) Abscissae of foci (c) Eccentricity (d) Directrix 31. The hyperbola is the conic with eccentricity (a) e > 1 (b) e < 1 (c) e =1 (d) 32. The eccentricity of the conic is (a) (b) (c) (d) 33. If be the eccentricities of two conics S and and if , then both S and can be (a) Ellipses (b) Parabolas (c) Hyperbolas (d) None of these 34. If be respectively the eccentricities of ellipse and hyperbola , then (a) (b) (c) (d) 35. The length of the latus rectum of the hyperbola is (a) (b) (c) (d) 36. The distance between the foci of a hyperbola is 16 and its eccentricity is , then the equation of hyperbola is (a) (b) (c) (d) 37. The equation of the hyperbola with vertices (3, 0) and (–3, 0) and semi-latus-rectum 4, is given by (a) (b) (c) (d) None of these 38. Equation of the hyperbola with eccentricity 3/2 and foci at is (a) (b) (c) (d) None of these 39. The eccentricity of the hyperbola with latus rectum 12 and semi-conjugate axis , is (a) 2 (b) 3 (c) (d) 40. The eccentricity of the hyperbola is (a) (b) (c) (d) 41. The equation represents (a) A hyperbola if (b) An ellipse if (c) A hyperbola if 8 < k < 12 (d) None of these 42. The auxiliary equation of circle of hyperbola is (a) (b) (c) (d) 43. A point on the curve is (a) (b) (c) (d) None of these 44. The locus of the point of intersection of the lines and where is the parameter, is (a) A straight line (b) A circle (c) An ellipse (d) A hyperbola 45. The eccentricity of the conic represented by is (a) 1 (b) (c) 2 (d) 1/2 46. The latus rectum of the hyperbola is (a) (b) 9 (c) (d) 47. The vertices of a hyperbola are at and and one of its foci is at . The equation of the hyperbola is (a) (b) (c) (d) 48. The equations of the transverse and conjugate axis of the hyperbola are (a) (b) (c) (d) None of these 49. Foci of the hyperbola are (a) (b) (c) (d) None of these 50. The eccentricity of the conic is (a) (b) (c) (d) 51. The equation represents a hyperbola (a) The length of whose transverse axis is (b) The length of whose conjugate axis is 4 (c) Whose centre is (–1, 2) (d) Whose eccentricity is 52. The equation of the hyperbola whose foci are and eccentricity is (a) (b) (c) (d) None of these 53. The equation represents (a) An ellipse (b) A parabola (c) A hyperbola (d) A circle 54. The vertices of the hyperbola are (a) (6, 3) and (–6, 3) (b) (6, 3) and (–2, 3) (c) (–6, 3) and (–6, –3) (d) None of these 55. The curve represented by is (a) A hyperbola (b) An ellipse (c) A parabola (d) A circle 56. The foci of the hyperbola are (a) (2, 3), (5, 7) (b) (4, 1), (–6, 1) (c) (0, 0), (5, 3) (d) None of these 57. The equations of the transverse and conjugate axes of a hyperbola respectively are , and their respective lengths are and . The equation of the hyperbola is (a) (b) (c) (d) 58. The points of intersection of the curves whose parametric equations are and is given by (a) (1, –3) (b) (2, 2) (c) (–2, 4) (d) (1, 2) 59. Equation represents (a) A rectangular hyperbola (b) A hyperbola (c) An ellipse (d) A parabola 60. The line touches the curve if (a) (b) (c) (d) 61. The line will be a tangent to the hyperbola if (a) (b) (c) (d) None of these 62. If the straight line be a tangent to the hyperbola then (a) (b) (c) (d) 63. The equation of the tangent at the point of the conic is (a) (b) (c) (d) None of these 64. If the line be a tangent to the hyperbola then (a) 16 (b) –16 (c) (d) None of these 65. The equation of the tangent to the hyperbola at the point (1, 0) is (a) (b) (c) (d) 66. The straight line will touch the hyperbola , is (a) (b) (c) (d) 67. The equation of the tangent to the hyperbola which is parallel to the line , is (a) (b) (c) and (d) None of these 68. The equation of tangents to the hyperbola which cuts equal intercepts from the axes, are (a) (b) (c) (d) 69. The line is a tangent to the hyperbola . The point of contact is (a) (3, 1) (b) (2, 1/4) (c) (1, 3) (d) None of these 70. The equation of a common tangent to the conics and is (a) (b) (c) (d) 71. The equation of common tangents to the parabola and hyperbola , is (a) (b) (c) (d) 72. The radius of the director circle of the hyperbola , is (a) (b) (c) (d) 73. The tangents to the hyperbola are parallel to the straight line at the following points. (a) (2, 1) or (1, 2) (b) (2, –1) or (–2, 1) (c) (–1, –2) (d) (–2, –1) 74. The line touches the hyperbola iff (a) (b) (c) (d) 75. The line touches the hyperbola at the point (a) (b) (c) (d) None of these 76. The number of tangents to the hyperbola from an external point is (a) 2 (b) 4 (c) 6 (d) 5 77. The slope of the tangent to the hyperbola at (3, 2)is (a) –1 (b) 1 (c) 0 (d) 2 78. A common tangent to and is (a) (b) (c) (d) None of these 79. The product of the perpendiculars from two foci on any tangent to the hyperbola (a) (b) (c) (d) 80. If the two intersecting lines intersect the hyperbola and neither of them is a tangent to it, then number of intersecting points are (a) 1 (b) 2 (c) 2, 3 or 4 (d) 2 or 3 81. The equation of a tangent parallel to drawn to is (a) (b) (c) (d) 82. The equation of the tangent to the conic at (2, 1) is (a) (b) (c) (d) 83. The equation of tangents to the hyperbola which are perpendicular to the line 0 (a) (b) (c) (d) None of these 84. The position of point (5, – 4) relative to the hyperbola (a) Outside the hyperbola (b) Inside the hyperbola (c) On the conjugate axis (d) On the hyperbola 85. If the two tangents drawn on hyperbola in such a way that the product of their gradients is , then they intersects on the curve (a) (b) (c) (d) None of these 86. C the centre of the hyperbola . The tangent at any point P on this hyperbola meets the straight lines and in the points Q and R respectively. Then (a) (b) (c) (d) 87. Let and , where , be two points on the hyperbola . If is the point of intersection of the normals at P and Q, then k is equal to (a) (b) (c) (d) 88. Let P be a point on the hyperbola where a is a parameter such that P is nearest to the line . The locus of P is (a) (b) (c) (d) 89. An ellipse has eccentricity and one focus at the point . Its one directrix is the common tangent nearer to the point P, to the circle and the hyperbola . The equation of the ellipse in the standard form, is (a) (b) (c) (d) 90. The condition that the straight line may be a normal to the hyperbola is given by (a) (b) (c) (d) 91. The equation of the normal to the hyperbola at (–4, 0) is (a) (b) (c) (d) 92. The equation of the normal at the point of the curve is (a) (b) (c) (d) 93. The number of normals to the hyperbola from an external point is (a) 2 (b) 4 (c) 6 (d) 5 94. The locus of the middle points of the chords of hyperbola parallel to is (a) (b) (c) (d) 95. The equation of the chord of the hyperbola which is bisected at is (a) (b) (c) (d) 96. If the chords of contact of tangents from two points and to the hyperbola are at right angles, then is equal to (a) (b) (c) (d) 97. Equation of the chord of the hyperbola which is bisected at the point (6, 2) is (a) (b) (c) (d) None of these 98. If is the chord of contact of the hyperbola , then the equation of the corresponding pair of tangent is (a) (b) (c) (d) 99. If and are the ends of a focal chord of , then equals to (a) (b) (c) (d) 100. If and cut at right angles, then (a) (b) (c) (d) 101. The locus of the middle points of the chords of contact of tangents to the hyperbola from points on the auxiliary circle, is (a) (b) (c) (d) None of these 102. The locus of the mid points of the chords of the hyperbola , which subtend a right angle at the origin (a) (b) (c) (d) None of these 103. The diameter of which is conjugate to is (a) (b) (c) (d) 104. The lines and may be conjugate w.r.t the hyperbola , if (a) (b) (c) (d) None of these 105. The polars of and w.r.t are perpendicular to each other if (a) (b) (c) (d) 106. The locus of the pole of normal chords of the hyperbola is (a) (b) (c) (d) None of these 107. The locus of the pole with respect to the hyperbola of any tangent to the circle, whose diameter is the line joining the foci is the (a) Ellipse (b) Hyperbola (c) Parabola (d) None of these 108. The product of the lengths of perpendicular drawn from any point on the hyperbola to its asymptotes is (a) (b) (c) (d) 2 109. The angle between the asymptotes of is equal to (a) (b) (c) (d) 110. The product of perpendicular drawn from any point on a hyperbola to its asymptotes is (a) (b) (c) (d) 111. From any point on the hyperbola tangents are drawn to the hyperbola . The area cut-off by the chord of contact on the asymptotes is equal to (a) (b) (c) (d) 112. The equation of the hyperbola whose asymptotes are the straight lines and and which passes through origin is (a) (b) (c) (d) None of these 113. The equation of the asymptotes of the hyperbola are (a) (b) (c) (d) None of these 114. Eccentricity of the curve is (a) 2 (b) (c) 4 (d) None of these 115. The eccentricity of curve is (a) (b) (c) 2 (d) 116. The eccentricity of the hyperbola is (a) (b) (c) 2 (d) 117. If transverse and conjugate axes of a hyperbola are equal, then its eccentricity is (a) (b) (c) (d) 2 118. The eccentricity of the hyperbola is (a) (b) (c) 2 (d) 119. Eccentricity of the rectangular hyperbola is (a) 2 (b) (c) 1 (d) 120. The reciprocal of the eccentricity of rectangular hyperbola, is (a) 2 (b) (c) (d) 121. The locus of the point of intersection of the lines and , where is the parameter, is (a) A circle (b) An ellipse (c) A rectangular hyperbola (d) None of these 122. Curve is said to be (a) Parabola (b) Rectangular hyperbola (c) Hyperbola (d) Ellipse 123. What is the slope of the tangent line drawn to the hyperbola at the point (a) (b) (c) (d) 124. The coordinates of the foci of the rectangular hyperbola are (a) (b) (c) (d) None of these 125. A tangent to a hyperbola intercepts a length of unity from each of the coordinate axes, then the point lies on the rectangular hyperbola (a) (b) (c) (d) None of these 126. A rectangular hyperbola is one in which (a) The two axes are rectangular (b) The two axes are equal (c) The asymptotes are perpendicular (d) The two branches are perpendicular 127. If and are the eccentricities of the hyperbolas and , then is equal to (a) 1 (b) 4 (c) 6 (d) 8 128. If the line is a normal to the curve xy = 1, then (a) (b) or (c) (d) None of these 129. The number of normals that can be drawn from any point to the rectangular hyperbola is (a) 1 (b) 2 (c) 3 (d) 4 130. The equation of the chord joining two points and on the rectangular hyperbola is (a) (b) (c) (d) 131. If a triangle is inscribed in a rectangular hyperbola, its orthocentre lies (a) Inside the curve (b) Outside the curve (c) On the curve (d) None of these 132. The equation of the common tangent to the curves and is (a) (b) (c) (d) 133. A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P,Q, R and S, then = (a) (b) (c) (d) 134. If and are four concyclic points on the rectangular hyperbola , the coordinates of orthocentre of the are (a) (b) (c) (d) 135. If a circle cuts the rectangular hyperbola in the points where then (a) (b) (c) (d)