Question

The normal to the curve x = a(1 + cos θ),

y = a sin θ at 'θ' point always passes through the fixed point –

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

Answer 1

Answer: (C)

(a, 0)

Answer 2

$\frac{dy}{dx}$ = – cot θ ⇒ slope of normal = tan θ

Equation of normal

y – a sin θ = tan θ (x – a – a cos θ)

y–\tan\theta(x–a) = 0 \end{matrix}$$ which is passing through (a, 0)