Question

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

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

Answer 1

Answer: (C)

We have, $x^2{y}^2=a^4\Rightarrow y^2=\frac{a^4}{x^2}$
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 $=\left|\frac{y}{dydx}\right|=\left|\frac{a}{1}\right|=a$