Surfaces in 3D

x²+y²+z²=r²

sphere with r (not r²) as the radius

x²/a² + y²/b² + z²/c²=r²

an ellipsoid with an x intercept of a, y intercept of b, and z intercept c (not a², b², or c²)

x²+y²=r² (with z = anything)

a cylinder spanning z

x²+z²=r² (with y = anything)

a cylinder spanning y

z=y²

a parabola spanning x

x²/a² + y²/b² = z²/c

a double cone with a & b as the “stretch” in their respective direction and c as the slope of the curve

z=sqrt(x²+y²)

half cone in the positive z direction

z=-sqrt(x²+y²)

half cone in the negative z direction

x²/a²+y²/b²=z/c

paraboloid with a and b as the “stretch” in their respective direction and c as the magnitude

z=sqrt(r²-x²-y²)

hemisphere in the positive z direction

z=-sqrt(r²-x²-y²)

hemisphere in the negative z direction

x=sqrt(r²-y²)

half cylinder spanning the z direction