Question

Question 6: If x and y are connected parametrically by the equation, without eliminating the parameter, find. x = a (θ – sin θ), y = a (1 + cos θ)

Class 12 - Math - Continuity and Differentiability

Answer 1

x = a (θ – sin θ)
y = a (1 + cos θ)

NOW
dx/dθ = d/dθ (aθ -asinθ )
dx/dθ = a - acosθ

dy/dθ = d/dθ (a+acosθ )
dy/dθ = -asinθ
dy/dx = asinθ /a(1-cosθ )
= sinθ /1-cosθ => -cotθ /2