My textbook uses the terms interchangably, and they look the same in graphs, so I was wondering if there a difference between the two? Thanks!
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$\begingroup$All circular paraboloids are elliptical paraboloids but not all elliptical paraboloids are circular paraboloids.
More precisely, an elliptical paraboloid in a surface which has parabolic cross sections in 2 orthogonal directions and 1 elliptical cross section in the other orthogonal direction.
(An elliptical paraboloid)
Because a circle is just a special type of ellipse (using one common definition of ellipse), a circular paraboloid (defined the same as elliptical paraboloid but with the last cross section being circular) is just a special type of elliptical paraboloid.
(A circular paraboloid)
If you'd prefer just to see the equations, the equation of an elliptical paraboloid is given by $$\frac zc = \left(\frac xa\right)^2 + \left(\frac yb\right)^2$$ If $a=b$, then this elliptical paraboloid is also a circular paraboloid.
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