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The number of points on the ellipse (x^2...

The number of points on the ellipse `(x^2)/(50)+(y^2)/(20)=1` from which a pair of perpendicular tangents is drawn to the ellipse `(x^2)/(16)+(y^2)/9=1` is (a)0 (b) 2 (c) 1 (d) 4

A

0

B

2

C

1

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
For the ellipse
`(x^(2))/(16)+(y^(2))/(9)=1`
the equation of director circle is `x^(2)+y^(2)=25`. The director circle will cut the ellipse
`(x^(2))/(50)+(y^(2))/(20)=1`
at four points. Hence,
Number of points =4
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