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If (x,y) lies on the ellipse x^(2)+2y^(3...

If `(x,y)` lies on the ellipse `x^(2)+2y^(3) = 2`, then maximum value of `x^(2)+y^(2)+ sqrt(2)xy - 1` is

A

`(sqrt(5)+1)/(2)`

B

`(sqrt(5)-1)/(2)`

C

`(sqrt(5)+1)/(4)`

D

`(sqrt(5)-1)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Any point on ellipse `x^(2) + 2y^(2) =2` is
`x = sqrt(2) cos theta, y = sin theta`
`alpha = x^(2) + y^(2) +sqrt(2) xy -1`
`= 2 cos^(2) theta + sin^(2) theta + sin 2 theta -1`
`=(1+cos 2 theta)/(2)+ sin 2 theta`
`alpha_(max) = (sqrt(5)+1)/(2)`
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