Survey of Quadric Surfaces

Ellipsoid

\(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} + \dfrac{z^2}{c^2}=1 \)

Hyperboloid of One Sheet

\(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} - \dfrac{z^2}{c^2}=1 \)

Hyperboloid of Two Sheets

\(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} - \dfrac{z^2}{c^2}= -1 \)

Paraboloid (Elliptic)

\(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = z \)

Paraboloid (Hyperbolic)

\(\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = z \)

Cone

\(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = \dfrac{z^2}{c^2} \)