Question

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

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

Answer 1

The correct option is B $(a,0)$

$x=a(1+\cos \theta )$ , $y=a\sin \theta$

Therefore, ${(x-a)}^2+y^2=a^2$

This represents the equation of a circle with center $(a,0)$.

All the normal to this curve will pass through the center of the circle, i.e., $(a,0)$.