Question

The normal to the curves x = a(1 + cosθ) and y = asinθ at angle θ always passes through the fixed point

(A) (a, a)

(B) (0, a)

(C) (0, 0)

(D) (a, 0)

Answer 1

Answer is (D) (a, 0)

The slope of the normal is

Now, the equation of normal at θ is

y - asinθ = tanθ[x - a(1 + cosθ)]

Clearly, this line passes through (a, 0).