How do I build a regular homotopy between an oval $$\frac{x^4}{a^4}+\frac{y^4}{b^4}=1$$ and a circle $$\ (x-x_0)^2+(y-y_0)^2=R^2$$?
I know I need to find parametrizations for both curves and there was a somewhat similar question discussed before Is this how to deform an ellipse into a circle in complex analysis?. However, I still don't get where all this comes from and what exactly to do to solve the problem.
Won't the obvious $$\bigl(x-x_0(1-t)\bigr)^{2(1+t)}+\bigl(y-y_0(1-t)\bigr)^{2(1+t)}=(a^4b^4-R^2)t+R^2$$ for $t\in\{0,1\}$work?