In a right triangle with sides x and y, hypotenuse z, the altitude drawn on the hypotenuse is a, then

x y = a^{2}

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\frac{1}{x} + \frac{1}{y} = \frac{1}{a}

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x^{2} + y^{2} = 2 a^{2}

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\frac{1}{x^{2}} + \frac{1}{y^{2}} = \frac{1}{a^{2}}

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Solution

The correct option is C $x^{2} + y^{2} = 2 a^{2}$
From the figure shown,
$x s i n m = a$ ....1
$y c o s m = a$ ....2
Squaring and adding 1 and 2,
$x^{2} + y^{2} = 2 a^{2}$

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x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y} = ?

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\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1,

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