Question

If x and y are connected parametrically by the equation, without eliminating the parameter, find `dy/dx.`

x = a (θ – sin θ), y = a (1 + cos θ)

Answer 1

Here c = a (θ - sinθ) 

y = a (1 + cosθ)

Differentiating (1) & (2) w.r.t.t t, we get

`dx/(dθ) = a [1 - cos θ]`

`dy/(dθ) = a [-sin θ]`

= -a sin θ

`dy/dx = (dy/(dθ))/(dx/(dθ)) = (-1 sin θ)/ (a (1 - cos θ))`

= `(- sin θ)/ (1- cos θ) = (-2 sin θ //2 cos θ//2)/(2 sin^2 θ//2)`

= `-cot  θ/2`