Combining Parametric Equations

Using the graph above we can see what happens when we add two sets of parametric equations together.[br][list][*]Curve 1: Shows/Hides the graph of [math]x_1\left(t\right)[/math] [math]y_1\left(t\right)[/math].[/*][*]Curve 2: Shows/Hides the graph of [math]x_2\left(t\right)[/math] [math]y_2\left(t\right)[/math].[/*][*]Sum: Shows/Hides the graph of their sum (the equation is shown at the upper right)[/*][*]Point Only: Shows/Hides just the point that is being traced out on the graph of the sum.[/*][*]Shadow of Curve 1 shows us how Curve 1 is being affected by the addition with Curve 2.[/*][/list][br]Options[br][list=1][*]Graph the Original Curve (Show Curve 1 only)[/*][*]Graph the Second Curve (Show Curve 2 only)[/*][*]Graph the Original Curve, translated by the second Curve (Show Curve 2, Shadow)[/*][*]Graph the point on the original curve as it is translated by the second curve (Show Curve 2, Shadow, Point)[/*][*]Graph the final curve of the sum (Show Sum)[/*][/list]

Information: Combining Parametric Equations