Practice Zone Maths : Ellipse

LEVEL – I

11. A tangent is drawn to the ellipse x2/27 + y2 = 1 at the point (3√3cosθ , sinθ) where 0 < θ < π/2 . The sum of intercepts of the tangent with the coordinate axes is least when θ equals

(A) π/6

(B) π/3

(C) π/8

(D) π/4

12. The area of the quadrilateral formed by the tangents to the ellipse x2/9 + y2/5 = 1 at the ends of the latus rectum is

(A) 27/4

(B) 9

(C) 27/2

(D) 27

13. P is any point on the ellipse and S and S’ are its foci, then maximum value of the angle SPS’ is

(A) π/4

(B) π/2

(C) 2 tan-1(ae/b)

(D) none of these

14. The curve with parametric equations x = 1 + 4 cosθ , y = 2 + 3 sin θ is

(A) an ellipse

(B) a parabola

(C) a hyperbola

(D) a circle

15. The eccentricity of an ellipse whose latus rectum is half of its major axis is

(A) 1/√2

(B) √(2/3)

(C) √3/2

(D) none of these

16. If base of a triangle is the major axis of the ellipse x2/16 + y2/9 = 1 and third vertex moves on the ellipse, then maximum area of triangle will be

(A) 6

(B) 72

(C) 12

(D) none of these

17. The locus of the point of intersection of the tangents drawn to the ellipse x2/4 + y2 = 1 if the difference of the eccentric angle of their point of contact is 2π/3 is

(A) x2/4 + y2 = 4

(B) x2/4 + y2 = 1

(C) 4x2 + y2 = 16

(D) none of these

18. The angle between ellipse x2/4 + y2 = 1 and circle x2 + y2 = 2 is θ , then tanθ is equal to

(A) 1/2

(B) 1/√2

(C) 1/2√2

(D) none of these

19. The locus of mid points of chords of an ellipse x2/4 + y2 = 1 the tangents at the extremities of which intersect at right angle is

(A) 16(x2 + y2)2 = 5(x2 + 4y2)

(B) 16(x2 + y2)2 = 5(x2 + 4y2)2

(C) 5(x2 + y2)2 = 16(x2 + 4y2)2

(D) none of these

20. Angle between tangents drawn from any point on the circle x2 + y2 = (a + b)2 to the ellipse
x2/a + y2/b = a + b is

(A) π/4

(B) tan-1(1/2)

(C) tan-1(1/3)

(D) none of these

ANSWER:

11. A  12. D  13. C  14. A  15. A  16. C  17. A  18. B   19. B  20. D  

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