Level Sets Equations

horizontal hyperbola & its orientation on graph

x²-y²=1 (opens left & right on x-axis)

line

y=x

vertical hyperbola & its orientation on graph

y²-x²=1 (opens up & down on y-axis)

elliptic paraboloid & its orientation on graph

z=x²+y² (opens upward to z-axis)

hyperbolic paraboloid & orientation on graph

z=x²-y² (opens upward in the x direction and downward in the y direction like a pringle - opposite of elliptic)

upper cone equation

z=√(x²+y²)

lower cone equation

z=-√x²+y²

standard (double cone)

x²+y²=z²

horizontal ellipse

x²/a²+y²/b²=1

vertical ellipse

x²/b²+y²/a²=1

equation to find vector of specified length

angle formula