If `x ,y in R ,` satisfies the equation `((x-4)^2)/4+(y^2)/9=1` , then the difference between the largest and the smallest valus of the expression `(x^2)/4+(y^2)/9` is_____

Answer

8

Explanation

`x-4=2costheta,y=sintheta`
`implies(x^(2))/4+(y^(2))/9=((2costheta+4)^(2))/4+(9sin^(2)theta)/9`
`=(costheta+2)^(2)+sin^(2)theta=5+4costhetaepsilon[1,9]`