Question

The length of the normal to the curve

x = a (q + sin q), y = a(1–cos q)at q = p/2 is

• A. 2a
• B. a/2
• C. $\sqrt{2}a$
• D. a/$\sqrt{2}$

Answer 1

Answer: (C)

$\sqrt{2}a$

Answer 2

Here $\frac{dy}{dx}$ = tan q/2 Ž ${\left( \frac{dy}{dx} \right)_{\theta}}_{= \frac{\pi}{2}}$ = tan $\left( \frac{\pi}{4} \right)$ = 1

at q = $\frac{\pi}{2}$, y = a (1 – cos $\frac{\pi}{2}$) = a

\ length of normal = y $\sqrt{1 + \left( \frac{dy}{dx} \right)^{2}}$

= a $\sqrt{1 + 1} = \sqrt{2}a$