If X² + Y² = t - 1 /t                   and X⁴ + Y⁴= t² +1/t²

then prove that dy / dx=1/X³Y

Given x²+y² = t-1/t. Squaring, we get x⁴+y⁴+2x²y² = t²+1/t² - 2

Also, given :

x⁴+y⁴ = t²+1/t²

Hence subtract the two to eliminate the parameter t :

2x²y² = -2

Differentiating now wrt x, we get dy/dx = 1/x³y

But answer is 1 / X³Y

See the solution: