Explanation

(c)
Given, $y^{2} = \frac{a^{4}}{x^{2}}$
$\Rightarrow \ \ \ \ \ \ 2y\frac{dy}{dx} = \frac{- 2a^{4}}{x^{3}}$
$\Rightarrow \ \ \ \ \ \ \frac{dy}{dx} = \frac{{- a}^{4}}{x^{3}y}$
At $(–a,\ a),\frac{dy}{dx} = \frac{- a^{4}}{- a^{3}.a} = 1$
Now, length of subtangent to the given curve at $( - a,\ a)$ is
$\frac{y}{dy/dx} = \frac{a}{1} = a$