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Q.

Number of points on the ellipse x250+y220=1from which pair of perpendicular tangents are drawn to the ellipse x216+y29=1 is

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a

4

b

2

c

5

d

1

answer is A.

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Detailed Solution

point on ellipse x250+y220=1 is 50 cosθ, 20 sinθ point lies on director circle of ellipse x216+y29=1

Director circle is  x2+y2=25

50 cos2θ+20 sin2θ=25 30cos2θ+20=25 cos2θ=530=16 cosθ=±16 director circle cuts ellipse at four distinct points   no. of points=4

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