### Distance element $ds^2$ in the elliptical coordinates

Find the distance element $ds^2$ in the elliptical coordinates $r=\sqrt{x^2/a^2+y^2/b^2}$, $\tan\varphi=y/x$. Define unit vectors tangential and normal to $r=\text{const}$ curves and derive their relation to $\hat{x}$ and $\hat{y}$.