Thread: Is this a cone or an ellipsoid?

I'm having some trouble figuring out if the equation z = 2 - sqrt(x^2 + y^2) is a cone, ellipsoid, or something else. If I simplify it to look like one of the forms by professor gave me, I get x^2 + y^2 - (2-z)^2 = 0, which looks like the cone formula. But if I go further it becomes ((x^2)/4) + ((y^2)/4) + ((z^2)/4) - (z/4) = 1, which makes it look like a kind of ellipsoid. Any help would be greatly appreciated and thank you in advance!

As well as comparing the shapes of the formulae you can try interpreting the equation visually. You can see the apex is at (0,0,2) (can you? I mean, you'll minimize the subtracted sqrt expression only by setting x and y to zero). Also, you can see that z is zero where x^2 + y^2 = 2^2... Also, over the x-axis, where y = 0, you have a straight line: z = 2 - x...

Ah, thank you Tom! I'm horrible at graphing equations, hopefully I can remember things like this for the test =p