# 10.1 - 1 10.1 Curves Dened by Parametric Equations Suppose...

• Notes
• 4

This preview shows page 1 - 4 out of 4 pages.

110.1 Curves Defined by Parametric EquationsSupposexandyare both given as functions oft(calledparameter) byx=f(t),y=g(t)(calledparametric equations).Astvaries, the point(x, y) = (f(t), g(t)) varies and traces out a curveC(calledparametric curve).Example1Sketch the curve defined by the parametricequationsx= 2t+t2,y=t-1.
In the following figure, we plot the points (x, y) determined byseveral values of the parametertand we join them to get a curve.51015-4-3-2-112xy
2Example2[Eliminating the parameter]Eliminate the parameter to identify the following para-metric curvex= 2t+t2,y=t-1
Example3What curve is represented by the paramet-ric equations?