1.

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

Answer»

`((sqrt6)/(sqrt5),(SQRT3)/(sqrt5))`
`(2,-1)`
`(-2, 1)`
`(-2, -1)`

SOLUTION :`P(sqrt6 cos theta, sqrt3 sin theta)` lies on ELLIPSE.
Normal at P is perpendicular to `x-y=7`
`therefore""1=-(sqrt6 cos theta)/(2sqrt3 sin theta), tan theta=(1)/(SQRT2), theta" line in "4^("th") " QUADRANT, "sin theta=-(1)/(sqrt3), cos theta=(sqrt2)/(sqrt3)`
`P(2, -1)`


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