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.
- 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)