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Ellipse

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  1. 101.The line 12x+5y=60 is tangent to which of the following curves?
  2. 102.The locus of mid-points of the line segments joining (-3,-5) and the points on the ellipse…
  3. 103.On the ellipse x^28+y^24=1, let P be a point in the second quadrant such that the tangent …
  4. 104.Let be the acute angle between the tangents to the ellipse x^29+y^21=1 and the circle x^2+…
  5. 105.The length of the minor axis (along the y-axis) of an ellipse in the standard form is 4√3.
  6. 106.If the distance between the foci of an ellipse is 6 and the distance between its directric…
  7. 107.If 3x+4y=12√2 is a tangent to the ellipse x^2a^2+y^29=1 for some a R, then the distance be…
  8. 108.Which of the following points lies on the locus of the foot of perpendicular drawn upon an…
  9. 109.Let x^2a^2+y^2b^2=1 (a>b) be a given ellipse, the length of whose latus rectum is 10.
  10. 110.Let x=4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is…
  11. 111.A hyperbola having the transverse axis of length √2 has the same foci as that of the ellip…
  12. 112.Let e_1 and e_2 be the eccentricities of the ellipse x^225+y^2b^2=1 (b<5) and the hyperbol…
  13. 113.Let S and S' be the foci of an ellipse and B be any one of the extremities of its minor ax…
  14. 114.Let the length of the latus rectum of an ellipse with its major axis along the x-axis and …
  15. 115.An ellipse, with foci at (0,2) and (0,-2) and minor axis of length 4, passes through which…
  16. 116.If the line x-2y=12 is tangent to the ellipse x^2a^2+y^2b^2=1 at the point (3,-92), then t…
  17. 117.In an ellipse, with centre at the origin, if the difference of the lengths of major axis a…
  18. 118.If the length of the latus rectum of an ellipse is 4 units and the distance between a focu…
  19. 119.The eccentricity of an ellipse having centre at the origin, axes along the coordinate axes…
  20. 120.Consider an ellipse, whose centre is at the origin and its major axis is along the x-axis.
  21. 121.If the tangent at a point on the ellipse x^227+y^23=1 meets the coordinate axes at A and B…
  22. 122.A hyperbola whose transverse axis is along the major axis of the conic x^23+y^24=4 and has…
  23. 123.The area (in sq.
  24. 124.If the distance between the foci of an ellipse is half the length of its latus rectum, the…
  25. 125.If OB is the semi-minor axis of an ellipse, F_1 and F_2 are its foci, and the angle betwee…
  26. 126.The equation of the circle passing through the foci of the ellipse x^216+y^29=1, and havin…
  27. 127.A point on the ellipse 4x^2+9y^2=36, where the normal is parallel to the line 4x-2y-5=0, i…
  28. 128.Let the equations of two ellipses be E_1:x^23+y^22=1 and E_2:x^216+y^2b^2=1.
  29. 129.If the foci of the ellipse x^216+y^2b^2=1 coincide with the foci of the hyperbola x^2144-y…
  30. 130.Equation of the ellipse whose axes are the axes of coordinates and which passes through th…
  31. 131.The equation of the hyperbola whose foci are (-2,0) and (2,0) and eccentricity is 2 is giv…
  32. 132.A focus of an ellipse is at the origin.
  33. 133.In an ellipse, the distance between its foci is 6 and the minor axis is 8.
  34. 134.An ellipse has OB as semi-minor axis, F and F' its foci, and the angle FBF' is a right ang…
  35. 135.The eccentricity of an ellipse, with its centre at the origin, is 12.
  36. 136.The foci of the ellipse x^216+y^2b^2=1 and the hyperbola x^2144-y^281=125 coincide.
  37. 137.In the ellipse, the distance between its foci is 6 and minor axis is 8.
  38. 138.A focus of an ellipse is at the origin.
  39. 139.The ellipse x^2 + 4y^2 = 4 is inscribed in a rectangle aligned with the coordinate axex, w…
  40. 140.Equation of the ellipse whose axes of coordinates and which passes through the point (-3,1…
  41. 141.STATEMENT-1 : An equation of a common tangent to the parabola [y^2 = 16 3 x] and the ellip…
  42. 142.An ellipse is drawn by taking a diameter of thec circle [( x - 1 )^2 + y^2 = 1] as its sem…
  43. 143.The locus of the foot of perpendicular drawn from the centre of the ellipse x^2 + 3y^2 = 6…
  44. 144.The eccentricity of an ellipse whose centre is at the origin is [1 2].
  45. 145.Consider an ellipse, whose center is at the origin and its major axis is along the x-axis.
  46. 146.If the length of the latus rectum of an ellipse is 4 units and the distance between a focu…
  47. 147.The tangent and normal to the ellipse 3x2 + 5y2 = 32 at the point P(2, 2) meet the x-axis …
  48. 148.If the line x -- 2y = 12 is tangent to the ellipse [x^2 a^2 + y^2 b^2 = 1] at the point [(…
  49. 149.Let S = [ ( x,y ) R^2:y^2 1 + r - x^2 1 - r ;r 1.] Then S represents :
  50. 150.If the normal to the ellipse 3x2 + 4y2 = 12 at a point P on it is parallel to the line, 2x…