Question

If x=[a(1-t^2)]/(1+t^2), y=2at/(1+t^2), show that dy/dx=(t^2-1)/2t

Answer 1

Given x = (1-t2)/(1+t2)

y = 2t/(1+t2)

Put t = tan θ

θ = tan-1 t

x = (1-tan2θ)/(1+tan2θ)

= cos 2θ

y = 2 tan θ/(1 + tan2 θ)

= sin 2θ

x2 = cos2 2θ

y2 = sin2 2θ

Adding both we get

x2 + y2 = 1

Differentiate w.r.t.x

2x + 2y(dy/dx) = 0

dy/dx = -2x/2y

= -x/y

Answer:

Step-by-step explanation: