5.2-ELLIPSE -02-(ASSIGNMENT)

1. If a bar of given length moves with its extremities on two fixed straight lines at right angles, then the locus of any point on bar marked on the bar describes a/an (a) Circle (b) Parabola (c) Ellipse (d) Hyperbola 2. If the eccentricity of an ellipse becomes zero, then it takes the form of (a) A circle (b) A parabola (c) A straight line (d) None of these 3. The locus of a variable point whose distance from is times its distance from the line is (a) Ellipse (b) Parabola (c) Hyperbola (d) None of these 4. If A and B are two fixed points and P is a variable point such that , where , then the locus of P is (a) A parabola (b) An ellipse (c) A hyperbola (d) None of these 5. Equation of the ellipse whose focus is directrix is and is (a) (b) (c) (d) None of these 6. The locus of the centre of the circle is (a) An ellipse (b) A circle (c) A hyperbola (d) A parabola 7. The equation represents (a) A circle (b) An ellipse (c) A hyperbola (d) A parabola 8. The equation represents an ellipse, if (a) (b) (c) (d) None of these 9. Equation of the ellipse with eccentricity and foci at is (a) (b) (c) (d) None of these 10. The equation of the ellipse whose foci are and one of its directrix is , is (a) (b) (c) (d) None of these 11. The equation of ellipse whose distance between the foci is equal to 8 and distance between the directrix is 18, is (a) (b) (c) (d) 12. The equation of the ellipse whose one of the vertices is and the corresponding directrix is , is (a) (b) (c) (d) None of these 13. The equation of the ellipse whose centre is at origin and which passes through the points and is (a) (b) (c) (d) 14. An ellipse passes through the point and its eccentricity is . The equation of the ellipse is (a) (b) (c) (d) 15. If the centre, one of the foci and semi- major axis of an ellipse be (0, 0), (0, 3) and 5 then its equation is (a) (b) (c) (d) None of these 16. The equation of the ellipse whose latus rectum is 8 and whose eccentricity is , referred to the principal axes of coordinates, is (a) (b) (c) (d) 17. The lengths of major and minor axes of an ellipse are 10 and 8 respectively and its major axis is along the y-axis. The equation of the ellipse referred to its centre as origin is (a) (b) (c) (d) 18. The equation of the ellipse whose vertices are and foci are is (a) (b) (c) (d) None of these 19. The latus rectum of an ellipse is 10 and the minor axis is equal to the distance between the foci. The equation of the ellipse is (a) (b) (c) (d) None of these 20. The eccentricity of the ellipse , is (a) (b) (c) (d) 21. Eccentricity of the conic is (a) (b) (c) (d) 22. Eccentricity of the ellipse is (a) (b) (c) (d) 23. The eccentricity of the ellipse is (a) (b) (c) (d) 24. For the ellipse , the eccentricity is (a) (b) (c) (d) 25. If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is (a) (b) (c) (d) 26. If the length of the major axis of an ellipse is three times the length of its minor axis, then its eccentricity is (a) (b) (c) (d) 27. The length of the latus rectum of an ellipse is of the major axis. Its eccentricity is (a) (b) (c) (d) 28. Eccentricity of the ellipse whose latus rectum is equal to the distance between two focus points, is (a) (b) (c) (d) 29. If the distance between the foci of an ellipse be equal to its minor axis, then its eccentricity is (a) (b) (c) (d) 30. The length of the latus rectum of the ellipse is (a) (b) (c) (d) 31. For the ellipse , the length of latus rectum is (a) (b) (c) (d) 32. The length of the latus rectum of the ellipse , is (a) (b) (c) (d) 33. In an ellipse, minor axis is 8 and eccentricity is . Then major axis is (a) 6 (b) 12 (c) 10 (d) 16 34. The distance between the foci of an ellipse is 16 and eccentricity is . Length of the major axis of the ellipse is (a) 8 (b) 64 (c) 16 (d) 32 35. If the eccentricity of an ellipse be , then its latus rectum is equal to its (a) Minor axis (b) Semi-minor axis (c) Major axis (d) Semi-major axis 36. If the distance between a focus and corresponding directrix of an ellipse be 8 and the eccentricity be , then the length of the minor axis is (a) 3 (b) (c) 6 (d) None of these 37. The sum of focal distances of any point on the ellipse with major and minor axes as 2a and 2b respectively, is equal to (a) 2a (b) (c) (d) 38. P is any point on the ellipse whose foci are S and S' . Then equals (a) 3 (b) 12 (c) 36 (d) 324 39. The foci of are (a) (b) (c) (d) 40. In an ellipse , the distance between the foci is (a) (b) (c) 3 (d) 4 41. The distance between the directrices of the ellipse is (a) 8 (b) 12 (c) 18 (d) 24 42. If the eccentricity of the two ellipse , and are equal, then the value of a/b is (a) (b) (c) (d) 43. The equation of the ellipse whose one focus is at (4, 0) and whose eccentricity is 4/5, is (a) (b) (c) (d) 44. S and T are the foci of an ellipse and B is an end of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is (a) (b) (c) (d) 45. If C is the centre of the ellipse and S is one focus, the ratio of CS to semi-major axis, is (a) (b) (c) (d) None of these 46. If , distance between foci = length of minor axis, then equation of ellipse is (a) (b) (c) (d) None of these 47. Line joining foci subtends an angle of 90° at an extremity of minor axis, then eccentricity is (a) (b) (c) (d) None of these 48. If foci are points and minor axis is of length 1, then equation of ellipse is (a) (b) (c) (d) 49. The eccentricity of the ellipse is (a) (b) (c) (d) 50. For the ellipse (a) The eccentricity is (b) The latus rectum is (c) A focus is (d) A directrix is 51. The sum of the distances of any point on the ellipse from its foci is (a) (b) (c) (d) None of these 52. The sum of the focal distances from any point on the ellipse is (a) 32 (b) 18 (c) 16 (d) 8 53. The distance of a focus of the ellipse from an end of the minor axis is (a) (b) 3 (c) 4 (d) None of these 54. The equation of ellipse in the form , given the eccentricity to be and latus rectum is (a) (b) (c) (d) 55. The equation of the ellipse with axes along the x-axis and the y-axis, which passes through the points P (4, 3) and Q (6, 2) is (a) (b) (c) (d) 56. P is a variable point on the ellipse with AA' as the major axis. Then the maximum value of the area of the triangle APA' is (a) ab (b) 2ab (c) (d) None of these 57. The latus rectum of the ellipse is 1/2 then is equal to (a) (b) (c) (d) None of these 58. An ellipse is described by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the necessary length of the string and the distance between the pins respectively in cm, are (a) (b) (c) (d) None of these 59. A man running round a race-course notes that the sum of the distances of two flag-posts from him is always 10 meters and the distance between the flag-posts is 8 meters. The area of the path he encloses in square metres is (a) 15 (b) 12 (c) 18 (d) 8 60. The equation , represents (a) An ellipse (b) A hyperbola (c) A circle (d) An imaginary ellipse 61. The radius of the circle having its centre at (0,3) and passing through the foci of the ellipse , is (a) 3 (b) 3.5 (c) 4 (d) 62. The centre of an ellipse is C and PN is any ordinate and are the end points of major axis, then the value of is (a) (b) (c) (d) 1 63. Let P be a variable point on the ellipse with foci at S and . If A be the area of triangle , then the maximum value of A is (a) 24 sq. units (b) 12 sq. units (c) 36 sq. units (d) None of these 64. The eccentricity of the ellipse which meets the straight line on the axis of x and the straight line on the axis of y and whose axes lie along the axes of coordinates, is (a) (b) (c) (d) None of these 65. If the focal distance of an end of the minor axis of an ellipse (referred to its axes as the axes of x and y respectively) is k and the distance between its foci is 2h, then its equation is (a) (b) (c) (d) 66. If (5, 12) and (24, 7) are the foci of a conic passing through the origin, then the eccentricity of conic is (a) (b) (c) (d) 67. The maximum area of an isosceles triangle inscribed in the ellipse with the vertex at one end of the major axis is (a) (b) (c) (d) None of these 68. The radius of the circle passing through the foci of the ellipse and having its centre (0, 3) is (a) 4 (b) 3 (c) (d) 69. The locus of extremities of the latus rectum of the family of ellipse is (a) (b) (c) (d) 70. The equation of the ellipse whose centre is (2,–3), one of the foci is (3, –3) and the corresponding vertex is (4, –3) is (a) (b) (c) (d) None of these 71. The equation of an ellipse, whose vertices are (2, –2), (2, 4) and eccentricity is (a) (b) (c) (d) 72. The equation of an ellipse whose eccentricity 1/2 is and the vertices are (4, 0) and (10, 0) is (a) (b) (c) (d) 73. For the ellipse (a) Centre is (2, –1) (b) Eccentricity is (c) Foci are(3, 1) and (–1, 1) (d) Centre is (1, –1), foci are (3, –1) and (–1, –1) 74. The eccentricity of the ellipse (a) 1/2 (b) 2/3 (c) 1/3 (d) 3/4 75. The eccentricity of the ellipse is (a) 4/5 (b) 3/5 (c) 5/4 (d) Imaginary 76. The eccentricity of the ellipse , is (a) (b) (c) (d) None of these 77. The eccentricity of the ellipse is (a) (b) (c) (d) 78. The eccentricity of the curve represented by the equation is (a) 0 (b) 1/2 (c) (d) 79. The centre of the ellipse , is (a) (0, 0) (b) (1, 1) (c) (1, 0) (d) (0, 1) 80. The centre of the ellipse is (a) (1, 3) (b) (2, 3) (c) (3, 2) (d) (3, 1) 81. Latus rectum of ellipse is (a) (b) (c) (d) 82. The length of the axes of the conic , are (a) (b) (c) (d) 83. Equations represent a conic section whose eccentricity e is given by (a) (b) (c) (d) 84. The curve with parametric equations is (a) An ellipse (b) A parabola (c) A hyperbola (d) A circle 85. The equations , represent (a) An ellipse (b) A parabola (c) A circle (d) A hyperbola 86. The curve represented by is (a) A circle (b) A parabola (c) An ellipse (d) A hyperbola 87. The equations represent (a) A circle (b) An ellipse (c) A parabola (d) A hyperbola 88. The eccentricity of the ellipse represented by is (a) (b) (c) (d) None of these 89. The set of values of a for which represents an ellipse is (a) 1< a < 2 (b) 0