MTH-250: Vectors and the Geometric Space

Ellipsoid

x²/a² + y²/b² + z²/c² = 1

All three squared, added, and equal to 1.

Elliptic Paraboloid

x²/a² + y²/b² - z/c = 0

One term not squared, others have the same sign, set equal to zero

Hyperbolic Paraboloid

x²/a² - y²/b² - z/c = 0

One term is not squared, other two have opposite signs, set equal to zero.

Cone

x²/a² + y²/b² - z²/c² = 0

All three terms squared, one is subtracted, set equal to zero.

Hyperboloid of One Sheet

x²/a² + y²/b² - z²/c² = 1

All three squared, equal to 1. One term is negative.

Hyperboloid of Two Sheets

-x²/a² - y²/b² + z²/c² = 1

All three terms are squared, set equal to 1. Two terms are negative.

First Derivative of Parametric

Second Derivative of Parametric

Area of Parametric

Arc Length of Parametric

First Derivative of Polar

Polar Formulas (List 4)

Polar Area

Polar Arc Length

Vector Projection