Question

If $x^3+y^3-3axy=0$, then $\frac{dy}{dx}$ equals

• 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. $\frac{x^2+ay}{ax-y^2}$

Answer 1

The correct option is A $\frac{ay-x^2}{y^2-ax}$

Given, $x^3+y^3-3axy=0$
On differentiating with respect to $x$, we get
$3x^2+3y^2\cdot \frac{dy}{dx}-3a(x\frac{dy}{dx}+y)=0$
$\Rightarrow 3(x^2-ay)+3\frac{dy}{dx}(y^2-ax)=0$
$\Rightarrow \frac{dy}{dx}=\frac{ay-x^2}{y^2-ax}$