Area of an ellipse
= Area of an ellipse
{title2=$\pi ab$}
The region $x^2/a^2+y^2/b^2\leq1$, $a,b>0$, has <area> $\pi ab$. The <linear map> $(u,v)\mapsto(au,bv)$ sends the unit disk onto that region and multiplies <area> by its <Jacobian determinant> $ab$.