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 ________.

Answer

9

Explanation

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`