$($Evolutes$)$ Compute the evolutes and plot the wave$-$fronts for the following curves in $R^2$ :

Hippopede: $(x^2+y^2{)}^2=a{x}^2+y^2,$ where $a0$ is a parameter;

Cubic curves: $y^2+x^3-ax=b,$ where a and $b$ are parameters

Explain the relation between the wave$-$fronts and the evolutes Huygens's principle$)$ for these examples. You may use any software such as Mathematica or GeoGebra.