If `x,y in R` and satisfy the equation `xy(x^(2)-y^(2))=x^(2)+y^(2)` where `xne0` then the minimum possible value of `x^(2)+y^(2)` is

Options

A. 1
B. 2
C. 4
D. 8

Answer

C

Explanation

`because x,yinR` and `xy(x^(2)-y^(2))=x^(2)+y^(2)`
Let `x=rcostheta,y=rsin thetaimpliesr^(4)sin theta cos theta(cos^(2)theta-sin^(2)theta)=r^(2)`
`impliesr^(2)(1)/(4)sin4theta=1impliesr^(2)=(4)/(sin4theta)ge4`
`therefore` Minimum value of `x^(2)+y^(2)` is 4.