Question

The length of the subtangent to the curv $x^2y^2 = a^4$ at $(-a, a)$ is

• A. $3a $
• B. $2 a $
• C. $a $
• D. $4a $

Answer 1

Answer: (C)

We have, $x^2y^2 = a^4 \Rightarrow \:\: y^2 = \frac{a^4}{x^2}$
Differentiating w.r.t. x, we get
$2y \frac{dy}{dx} = \frac{-2a^{4}}{x^{3}}$
$ \left[\frac{dy}{dx}\right]_{\left(-a,a\right)} = \frac{-2a^{4}}{2\left(-a\right)^{3}.a}=1 $
Length of subtangent $= \left|\frac{y}{dy dx}\right| =\left|\frac{a}{1}\right|=a $