I am quite new to differential equations and derivatives. I want to derive an differential form for equation of an ellipse. If i start with an ordinary ellipse equation
\begin{equation} \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \end{equation}
How do i derive it then to get this form
$ -\frac{dx}{dy} = \frac{a^2}{b^2} \frac{y}{x} $
I would need an equation and some brief explanation on the procedure.