QUADRIC FUNCTIONS (CALC III/MATH 241 UIUC)

ELLIPTIC PARABOLOID

z/c = x^2/a^2 + y^2/b^2

HYPERBOLIC PARABOLOID

z/c = x^2/a^2 - y^2/b^2
z/c = y^2/b^2 - x^2/a^2

ELLIPSOID

x^2/a^2 + y^2/b^2 + z^2/c^2 = 1

DOUBLE CONE

z^2 = x^2 + y^2

HYPERBOLOID OF ONE SHEET

x^2/a^2 + y^2/b^2 - z^2/c^2 = 1

HYPERBOLOID OF TWO SHEETS

-x^2/a^2 - y^2/b^2 + z^2/c^2 = 1

HYPERBOLA (HORIZONTAL TRANSVERSE)

x^2 - y^2 = 1

HYPERBOLA (VERTICAL TRANSVERSE)

y^2 - x^2 = 1