Combining Parametric Equations

Using the graph above we can see what happens when we add two sets of parametric equations together.
  • Curve 1: Shows/Hides the graph of .
  • Curve 2: Shows/Hides the graph of .
  • 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.
  1. Graph the Original Curve (Show Curve 1 only)
  2. Graph the Second Curve (Show Curve 2 only)
  3. Graph the Original Curve, translated by the second Curve (Show Curve 2, Shadow)
  4. Graph the point on the original curve as it is translated by the second curve (Show Curve 2, Shadow, Point)
  5. Graph the final curve of the sum (Show Sum)