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If 4(x-sqrt2)^(2)+lambda(y-sqrt3)^(2)=45...

If `4(x-sqrt2)^(2)+lambda(y-sqrt3)^(2)=45 and (x-sqrt2)^(2)-4(y-sqrt3)^(2)=5` cut orthogonally, then integral value of `lambda` is ________.

Text Solution

Verified by Experts

The correct Answer is:
9
Ellipse `((x-sqrt2)^(2))/(45//4)-((y-sqrt3)^(2))/(45//lambda)=1" cut orthogonally."`
So, conics are confocal.
`therefore" "(45)/(4)-(45)/(lambda)=5+(5)/(4)`
`therefore" "lambda=9`
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