(553, #35) A curve, called the witch of Maria Agnesi, consists of all points P determined as shown in the figure. Show that parametric equations can be written as
.
Then sketch the curve.

Solution: First, from the right triangle whose vertices are (0,0), (0,2a), and (x,2a),

so
.

Second,let be the length of the line from (0,0) to A. From the right triangle whose vertices are (0,0), D, and A

so
.

Third, from the right triangle whose vertices are (0,0), (0,2a), and A

.

Consequently

This is the witch:

Maple Code

by: gm