Question

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

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

Answer 1

Answer: (A)

(a, 0)

Answer 2

$\frac{dx}{d\theta}$ = – a sin q**,** $\frac{dy}{d\theta} = a\cos\theta$; $\frac{dy}{dx} = - \frac{\cos\theta}{\sin\theta}$

equation y – a sin q =$\frac{\sin\theta}{\cos\theta}$ [x – a (1 + cos q)]

Ž (x – a) sin q – y cos q = 0

Ž which passes through (a, 0)