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

(A) $3 a$

(B) $2 a$

(C) $a$

(D) $4 a$

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Best answer

**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).**

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