Explanation

(c)
Equation of the curve is $x^{2}y^{2} = a^{4}$
On differentiating w.r.t. $x$, we get
$x^{2}2y\frac{dy}{dx} + y^{2}2x = 0$
$\Rightarrow \ \ \frac{dy}{dx} = \frac{- y}{x}$
$\Rightarrow \ \ \ \left( \frac{dy}{dx} \right)_{( - a,a)} = - \left( \frac{a}{- a} \right) = 1$
Therefore, length of subtangent at the point $( - a,\ a)$
$= \frac{y}{\left( \frac{dy}{dx} \right)} = \frac{a}{1} = a$