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Q.

If $x^{3} + y^{3} = 3 a x y$ then $\frac{d y}{d x} =$

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a

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

b

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

c

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

d

none of these

answer is A.

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Detailed Solution

$x^{3} + y^{3} = 3 a x y$

$3 x^{2} + 3 y^{2} \frac{d y}{d x} = 3 a [x \frac{d y}{d x} + y]$

$\frac{d y}{d x} (3 y^{2} - 3 a x) = 3 a y - 3 x^{2}$

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

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