Elliptic Paraboloid

The equation which is given here is the equation of an elliptic paraboloid.

x²/a² + y²/b² = z/c

Like with cylinders this has a cross section of an ellipse and if a = b it will comprise a cross section of a circle. While we deal with these we'll usually be dealing with the type that has a circle for a cross section.

 Here is a diagram of a typical elliptic paraboloid.

In this type of case the variable that isn't squared find outs the axis upon which the paraboloid opens up. As well, the sign of c will determine the direction that the paraboloid opens.  If c is positive after that it opens up and if c is negative then it opens down.