1.

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

Answer»

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


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