The implicit equation $x^{2}+5 x y+y^{2}-2 x+y-6=0$, then find $\frac{d y}{d x}$ at $(1,1)$
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The implicit equation $x^{2}+5 x y+y^{2}-2 x+y-6=0$, then find $\frac{d y}{d x}$ at $(1,1)$

(1) $\frac{5}{8}$

(2) $-\frac{5}{8}$

(3) $\frac{8}{5}$

(4) $-\frac{8}{5}$

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SOLUTION —

$\frac{d y}{d x}=-\frac{\frac{\partial f}{\partial x}}{\frac{\partial f}{\partial y}}$

$=-\frac{2 x+5 y-2}{5 x+2 y+1}=\frac{-5}{8}$ at $(1,1)$

So, The correct option will be (2).

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