Question

The normal to the curve $x=a(1+\cos \theta )$, $y=a\sin \theta$ at the point ${}^{\prime }{\theta }^{\prime }$ always passes through the fixed point

• A. $(a,0)$
• B. $(0,a)$
• C. $(0,0)$
• D. $(a,a)$

Answer 1

Answer: (A)

$(a,0)$

Here $x=a(1+\cos \theta ),y=a\sin \theta$
Eliminating $\theta$ from above equations we get,
$(x-a{)}^2+y^2=a^2$.
Clearly this is a circle, and normal to the circle always passes through it's centre which is $(a,0)$