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If x^2+y^2=x^2y^2 then find the range of...

If `x^2+y^2=x^2y^2` then find the range of `(5x+12 y+7x y)/(x y)` .

Text Solution

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We have `x^(2)+y^(2)=x^(2)y^(2)` or `((1)/(x))^(2)+((1)/(y))^(2)=1`
Let `x=sec theta "and" y=co sec theta`
`rArr (5x+12y+7xy)/(xy)=5sin theta+12 cos theta+7 in [-6,20]`
`therefore (5x+12y+7xy)/(xy)in[-6,20]`
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