The point on the ellipse x^(2)+2y^(2)=6...

The point on the ellipse `x^(2)+2y^(2)=6` which is nearest to the line `x-y=7` is

A

`((sqrt(6))/(sqrt(5)),(sqrt(3))/(sqrt(5)))`

B

`(2,-1)`

C

`(-2,1)`

D

`(-2,-1)`

Verified by Experts

The correct Answer is:

B

`P( sqrt(6) cos theta, sqrt(3) sin theta)` lies on ellipse.
Normal at P is perpendicular to `x-y=7` `P(2,-1)`

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