AP Calculus BC glossary

Eliminating the parameter

Eliminating the parameter converts a pair of parametric equations into one equation relating x and y directly. Solve one equation for the parameter and substitute into the other, or use an identity when the equations are trigonometric.

For $x = \cos t$ and $y = \sin t$ , the Pythagorean identity gives $x^{2} + y^{2} = 1$ without solving for $t$ at all.

The mistake

Losing the restriction on the curve. The parametric form may trace only part of the resulting graph, and it also carries a direction that the x-y equation cannot express.

Appears in: Unit 9: Parametric, Polar, and Vector (BC)