Question

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

• A. $\frac{ay-y^2}{x^2-ax}$
• B. $\frac{ay-x^2}{y^2-ax}$
• C. $\frac{by-x^2}{y^2-bx}$
• D. None of these

Answer 1

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

Given that
$x^3+y^3=3axy$
We have to find $\frac{dy}{dx}$
Differentiate w r to $x$
$\frac{d}{dx}(x^3+y^3-3axy)=0$
$3x^2+3y^2\frac{dy}{dx}-3a\left(x\frac{dy}{dx}+y\right)=0$
$3x^2+3y^2\frac{dy}{dx}-3ax\frac{dy}{dx}-3ay=0$
Dividing throughout by $3$
$\frac{dy}{dx}(y^2-ax)=ay-x^2$
$\frac{dy}{dx}=\frac{ay-x^2}{y^2-ax}$