The envelope of lines form an ellipse
The applet below shows vertical lines at You can change the locations of these lines by moving the blue point. We want to see the envelope of lines joining to for all nonzero y-values. In the applet, the blue lines start from evenly-spaced points on the line and the red lines start from evenly-spaced points on As you can see, the envelope of these lines is an ellipse (and a circle when ).