# Quizzes : Ellipse

QUIZ – II
31. The range of eccentricity of ellipse $\large \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$  (a > b) such that line segment joining the foci does not subtend a right angle at any point on the ellipse is

(A) (0 ,1/2)

(B) (0 ,1/√2)

(C) (0 ,3/4)

(D) none of these

Ans: (B)

32. Tangents at the extremities of latus rectum of an ellipse intersect on

(A) tangent at vertex

(B) directrix

(C) the line y = x

(D) none of these

Ans: (B)

33. From a point P chords are drawn to the ellipse $\large \frac{x^2}{4} + \frac{y^2}{3} = 1$  , to cut it at R and S. If tangents at R and S always met in the line 2x + 4y = 1 , then coordinates of the point P are

(A) (8, 6)

(B) (6, 8)

(C) (- 6, 8)

(D) (8, 12)

Ans: (D)

34. If normal at any point P to the ellipse $\large \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ (a > b) meet the axes at M and N so that , then the value of eccentricity is

(A) 1/√2

(B) √2/ √3

(C) 1/ √3

(D) none of these

Ans: (C)

35. If the line joining foci subtends an angle of 90° at an extremity of minor axis then the eccentricity of the ellipse is

(A) 1/√3

(B) (1/√2)

(C) 1/2

(D) none of these

Ans: (B)

36. The eccentricity of the ellipse 12x2 + 4y2 + 12x – 16y + 25 = 0 is

(A) √(2/3)

(B) √(1/2)

(C) √(1/3)

(D) none of these

Ans: (A)

37. An ellipse has directrix x + y = 2 focus at (3, 4) eccentricity = 1/2 , then length of latus rectum is

(A) 5/2

(B) 5/√2

(C) 5√2

(D) none of these

Ans: (B)

38. If the eccentricity of an ellipse be 2/3 and its latus rectum is 2/3 , then equation of ellipse will be

(A) 25x2 + 45y2 = 9

(B) 25x2 – 45y2 = 9

(C) 25x2 – 4y2 = -9

(D) none of these

Ans: (A)

39. The length of sides of square which can be made by four perpendicular tangents to the ellipse $\large \frac{x^2}{7} + \frac{y^2}{11} = 1$   is

(A) 4

(B) 5

(C) 6

(D) none of these

Ans: (B)

40. An ellipse is described by using an end less 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 pins respectively in cms are

(A) 6,2√5

(B) 6,√5

(C) 4,2√5

(D) none of these

Ans: (A)

41. The eccentricity of the ellipse which meets the straight line x/7 + y/2 = 1 on the axis of x and the straight line x/3 – y/5 = 1 on the axis of y and whose axis lie along the axes of co-ordinates is

(A) 3√2/7

(B) 2√6/7

(C) 2√3/7

(D) none of these

Ans: (B)

42. The point on the ellipse x2 + 2y2 = 6 closest to the line x + y = 7

(A) (1, 2)

(B) (2, 1)

(C) (3, 2)

(D) none of these

Ans: (B)

43. A ray emanating from the point (-4, 0) is incident on the ellipse 9x2 + 25y2 = 225 at the point P with ordinate 3. The equation of the reflected ray after first reflection is

(A) 3x + 4y = 10

(B) 3x + 4y = 12

(C) 4x + 3y = 12

(D) none of these

Ans: (B)

44. If straight line ax/3 + by/4 = c is a normal to the ellipse $\large \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$   (a > b), then a2 – b2 is equal to

(A) 4c

(B) 5c

(C) 6c

(D) none of these

Ans: (B)

45. The equation of normal to the ellipse x2 + 4y2 = 9 at the point where the eccentric angle is π/4 is

(A) 4x – 2y = 9

(B) 4√2x – 2√2y = 9

(C) 4√2x – √2y = 9

(D) none of these

Ans: (B)

46. If tangent at P(a cosθ, b sinθ) on ellipse $\large \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ (a > b) meets major axis and minor axis at A and B respectively, then AB is minimum when tanθ is equal to

(A) √(a/b)

(B) √(b/a)

(C) a/b

(D) none of these

Ans: (B)

47. Maximum length of perpendicular from centre of ellipse $\large \frac{x^2}{9} + \frac{y^2}{4} = 1$   on any normal to this ellipse is equal to a + 5, then value of a is

(A) – 4

(B) – 3

(C) 4

(D) none of these

Ans: (A)

48. The locus of point of intersection P of tangents to ellipse 2x2 + 3y2 = 6 at A and B if AB subtend 90° angle at centre of ellipse is an ellipse whose eccentricity is equal to

(A) √5/4

(B) √5/3

(C) 2/ √5

(D) none of these

Ans: (B)

49. If 4x – 3y = 7 is a normal to ellipse $\large \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$   (a > b) whose eccentricity is , then a + b is equal to

(A) 7√2

(B) 5√2

(C) 3√2

(D) none of these

Ans: (A)

50. If S and S’ are the focii of the ellipse $\large \frac{x^2}{25} + \frac{y^2}{16} = 1$   and P is any point on it, then difference of maximum and minimum of SP.S’P is equal to

(A) 16

(B) 9

(C) 15

(D) 25