Elliptic paraboloid
= Elliptic paraboloid
{title2=$z=x^2/A^2+y^2/B^2$}
An elliptic paraboloid is a smooth bowl-shaped quadratic surface with elliptical horizontal sections. In the circular case $A=B$, it is a <surface of revolution>. For $z=x^2+y^2$, polar coordinates give the parametrization $(r\cos\theta,r\sin\theta,r^2)$ and upward <vector area element> $(-2r^2\cos\theta,-2r^2\sin\theta,r)\,dr\,d\theta$. A band between two positive heights has two boundary circles and no cap.