The normal to the curve `x=a(1+cos theta), y=a sin theta " at " 'theta ' ` always passes through the fixed point

Options

A. `(a,0)`
B. `(0,a)`
C. `(0,0)`
D. `(a,a)`

Answer

A

Explanation

Given `x=a(1+cos theta),y=a sin theta`
`implies(dx)/(d theta)=a(-sin theta),(dy)/(d theta) =a cos theta`
`:.(dy)/(dx)=(-cos theta)/(sin theta)`
Equation of normal at thegiven point is
`y-a sin theta=(sin theta)/(cos theta)[x-a(1+cos theta)]`
It is clear that int he given options normal passes through the point `(a,0)`.