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The points on the ellipse (x^(2))/(2)+(y...

The points on the ellipse `(x^(2))/(2)+(y^(2))/(10)=1` from which perpendicular tangents can be drawn to the hyperbola `(x^(2))/(5)-(y^(2))/(1) =1` is/are

A

`(sqrt((3)/(2)),sqrt((5)/(2)))`

B

`(sqrt((3)/(2)),-sqrt((5)/(2)))`

C

`(-sqrt((3)/(2)),sqrt((5)/(2)))`

D

`(sqrt((5)/(2)),sqrt((3)/(2)))`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Required points will lie on the intersection of ellipse `(x^(2))/(2)+(y^(2))/(10)=1` with director circle of hyperbola `(x^(2))/(5)-(y^(2))/(1) =1` i.e. on `x^(2) + y^(2) =4`
`rArr (sqrt(2)cos theta)^(2) + (sqrt(10)sin theta)^(2) =4`
Solving, we get `sin theta = +- (1)/(2), cos theta = +-(sqrt(3))/(2)`
`:.` Points are `(+-sqrt((3)/(2)),+-sqrt((5)/(2)))`
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