A) \[\frac{ay-{{x}^{2}}}{{{y}^{2}}-ax}\]
B) \[\frac{ay-{{x}^{2}}}{ay-{{y}^{2}}}\]
C) \[\frac{{{x}^{2}}+ay}{{{y}^{2}}+ax}\]
D) \[\frac{{{x}^{2}}+ay}{ax-{{y}^{2}}}\]
Correct Answer: A
Solution :
\[{{x}^{3}}+{{y}^{3}}-3axy=0\] Differentiate w.r.t. x, \[3{{x}^{2}}+3{{y}^{2}}.\frac{dy}{dx}-3a\left( x\frac{dy}{dx}+y \right)=0\] \[3({{x}^{2}}-ay)+3\frac{dy}{dx}({{y}^{2}}-ax)=0\]\[\Rightarrow \]\[\frac{dy}{dx}=\frac{ay-{{x}^{2}}}{{{y}^{2}}-ax}\].
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