If x4+7x2y2+9y4=24xy3 then dydx=

x4+7x2y2+9y4=24xy3 (xy)4+7(xy)2−24(xy)+9=0 4(xy)3(y−xy1y2)+7(2)(xy)(y−xy1y2)−24(y−xy1y2)=0 y−xy1y2=0⇒y−x⋅y1=0⇒ dydx=yx

If x4+7x2y2+9y4=24xy3 then dydx=

x4+7x2y2+9y4=24xy3 (xy)4+7(xy)2−24(xy)+9=0 4(xy)3(y−xy1y2)+7(2)(xy)(y−xy1y2)−24(y−xy1y2)=0 y−xy1y2=0⇒y−x⋅y1=0⇒ dydx=yx

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If $x^{4} + 7 x^{2} y^{2} + 9 y^{4} = 24 x y^{3}$ then $\frac{d y}{d x} =$

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- \frac{y}{x}

- \frac{x}{y}

\frac{x}{y}

\frac{y}{x}

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Detailed Solution

x^{4} + 7 x^{2} y^{2} + 9 y^{4} = 24 x y^{3}

${(\frac{x}{y})}^{4} + 7 {(\frac{x}{y})}^{2} - 24 (\frac{x}{y}) + 9 = 0$

$4 {(\frac{x}{y})}^{3} (\frac{y - x y^{1}}{y^{2}}) + 7 (2) (\frac{x}{y}) (\frac{y - x y^{1}}{y^{2}}) - 24 (\frac{y - x y^{1}}{y^{2}}) = 0$

$\frac{y - x y^{1}}{y^{2}} = 0 \Rightarrow y - x \cdot y^{1} = 0 \Rightarrow \frac{d y}{d x} = \frac{y}{x}$

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If $x^{4} + 7 x^{2} y^{2} + 9 y^{4} = 24 x y^{3}$ then $\frac{d y}{d x} =$