The length of the subtangent to the curve x^{ | vedclass

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(C) Given the curve $x^{2} y^{2} = a^{4}$.Taking the derivative with respect to $x$:$2x y^{2} + 2x^{2} y \frac{dy}{dx} = 0$.At the point $(-a, a)$:$2(

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$a$

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(C) Given the curve $x^{2} y^{2} = a^{4}$.Taking the derivative with respect to $x$:$2x y^{2} + 2x^{2} y \frac{dy}{dx} = 0$.At the point $(-a, a)$:$2(-a)(a)^{2} + 2(-a)^{2}(a) \frac{dy}{dx} = 0$.$-2a^{3} + 2a^{3} \frac{dy}{dx} = 0$.$2a^{3} \frac{dy}{dx} = 2a^{3} \implies \frac{dy}{dx} = 1$.The length of the subtangent is given by the formula $\left| \frac{y}{dy/dx} \right|$.Substituting the values $y = a$ and $\frac{dy}{dx} = 1$:Length of subtangent $= \left| \frac{a}{1} \right| = a$.

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

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