The length of the subtangent to the curve x^2 | vedclass

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(C) The equation of the curve is $x^2 y^2 = a^4$. Differentiating both sides with respect to $x$,we get: $x^2 \cdot 2y \frac{dy}{dx} + y^2 \cdot 2x =

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$a$

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(C) The equation of the curve is $x^2 y^2 = a^4$. Differentiating both sides with respect to $x$,we get: $x^2 \cdot 2y \frac{dy}{dx} + y^2 \cdot 2x = 0$ $\frac{dy}{dx} = -\frac{2xy^2}{2x^2y} = -\frac{y}{x}$ At the point $(-a, a)$,the slope of the tangent is: $\left( \frac{dy}{dx} ight)_{(-a, a)} = -\frac{a}{-a} = 1$ The length of the subtangent is given by the formula $\left| \frac{y}{dy/dx} ight|$. Substituting the values,we get: $	ext{Subtangent} = \left| \frac{a}{1} ight| = a$.

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

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