Parametric Equations: Fresh Take

  • Find a rectangular equation for a curve defined parametrically.
  • Find parametric equations for curves defined by rectangular equations.

Eliminating the Parameter

The Main Idea 

Sometimes you want to figure out what familiar curve your parametric equations represent. Eliminating the parameter means getting rid of [latex]t[/latex] to find a direct relationship between [latex]x[/latex] and [latex]y[/latex].

The Basic Strategy: Solve one parametric equation for [latex]t[/latex], then substitute that expression into the other equation. Choose whichever equation makes the algebra easier.

Eliminate the parameter for the plane curve defined by the following parametric equations and describe the resulting graph.

[latex]x\left(t\right)=2+\frac{3}{t},y\left(t\right)=t - 1,2\le t\le 6[/latex]

 

You can view the transcript for “BC Calculus: Eliminating the Parameter with Parametric Equations” here (opens in new window).

Find two different sets of parametric equations to represent the graph of [latex]y={x}^{2}+2x[/latex].

You can view the transcript for “Find Two Parametric Equations for the Given Rectangular Equation” here (opens in new window).