finding a parametric equation of a curve formed by deforming an ellipse

Question

I have a deformed curve from ellipse with the following form: $$\left( \frac{x}{a} \right)^2+\left( \frac{y}{b} \right)^2-\alpha\left(\frac{x}{a}\frac{y}{b}\right)^2=1,$$ where for $\alpha=0$ we get an ellipse, I know for ellipse the parametric equation has the following form $$x=a\ cos(\theta)\ ;\ y=b\ sin(\theta)$$ where $\theta \in [0,2\pi]$, I am wondering how to include the effect of the coupled term $\alpha\left(\frac{x}{a}\frac{y}{b}\right)^2$.