# How to determine parabolic object.

This is more of an mathematics application question than anything, but.
Let's say I'm building a satellite or some sort of focusing device. I obviously need a parabola. If I have an object that resembles a parabola—for example, a pot of some sort—how can I determine that's it's in reality a parabola, and not just a random shape?
Also, what would I need to do to find the area inside of that pot?
Thanks.

You mean a paraboloid?

It should have the following equation

$$f(x,y) = a(x - x_0)^2 + b(y - y_0)^2 + k$$

Yep.
So I would measure out it's parameters, and say, mark a point as the origin? Then (let's assume inches instead of cm), mark another point on the edge and find it's coordinates? Would I keep doing that until I had an equation, then plug in values and make sure it fit roughly?

Office_Shredder
Staff Emeritus