Question

If x = a((1 + t²)/(1 - t²)) and y = 2t/(1 - t²) find dy/dx.

Answer 1

Here, x = a((1 + t²)/(1 - t²)) = a(-1 + (2/(1 - t²)))

∴ dy/dt = a(0 + 2 x(-1/(1 - t²)²).(-2t)) = 4at/(1 - t²)²

and y = 2t/(1 - t²)

∴ dy/dx = ((1 - t)².2 - 2t.(-2t))//(1 - t²)² = 2(1 + t²)/(1 - t²)²

∴ dy/dx = (dy/dt)/(dx/dt) = (2(1 + t²)/(1 - t²)²) x ((1 - t²)²/4at)

= (1 + t²)/2at