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Global Maxima

The length of...

Question

The length of sub normal to the curve $x y = a^{2}$ at (x,y) on it varies at

x^{2}

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y^{2}

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x^{3}

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y^{3}

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Solution

The correct option is C $y^{3}$
Given,

$x y = a^{2}$

$\Rightarrow x \frac{d y}{d x} + y = 0$

$∴ \frac{d y}{d x} = - \frac{y}{x}$

Now,

Sub normal $= y \frac{d y}{d x}$

$= y (- \frac{y}{x})$

$= - \frac{y^{2}}{x}$

$= - \frac{y^{2}}{\frac{a^{2}}{y}}$

$= - \frac{y^{3}}{a^{2}}$

$∴ S N \propto y^{3}$

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