# 2D Parametric Curves

- Author:
- Dr. Jack L. Jackson II

## 2D Parametric Curves

You will want to open this activity in the app to be able to see all three windows and to turn on and off the visibility of the windows. Click on the three vertical dots in the top right and select Open in App.
Enter formulas for x and y in terms of the parameter t. The graph on the left shows the functions graphed individually with the horizontal axis being the t-axis and the vertical axis representing the output of x or y, depending on which function you are observing. The graph in the middle (Graphics View 1) is the graph of the parametric function. The spreadsheet shows a table of input-output values. Consider t time and the pink point is traveling along the blue path as time changes. Check the checkboxes to see related vectors. These include the position vector from the origin, and the velocity, and acceleration vectors for the point. The unit tangent vector points in the direction of the motion, while the unit normal vector is perpendicular to this. The speed, curvature, magnitude of the acceleration, and the length of the curve are all computed and displayed. The checkbox for Circle gives the osculating circle, which has the same curvature as the curve.