SOLUTION —
$\begin{array}{l}\text { On differentiating the given equation, we get } \\\begin{aligned}x^2 2 y \frac{d y}{d x}+y^2 2 x & =0 \\\Rightarrow \quad \frac{d y}{d x} & =\frac{-y}{x} \\\Rightarrow \quad\left(\frac{d y}{d x}\right)_{(-a, a)} & =-\left(\frac{a}{-a}\right)=1\end{aligned}\end{array}$
Therefore, subtangent at the point $(-a, a)$
$=\frac{y}{\left(\frac{d y}{d x}\right)}=\frac{a}{1}=a$
So, The correct option will be (C).