The bell-shaped witch of Maria Agnesi can be constructed in the following way. Start with a circle of radius 1, centered at the point (0, 1), as shown in the accompanying figure. Choose a point A on the line y = 2 and connect it to the origin with a line segment. Call the point where the segment crosses the circle B. Let P be the point where the vertical line through A crosses the horizontal line through B. The witch is the curve traced by P as A moves along the line y = 2. Find parametric equations and a parameter interval for the witch by expressing the coordinates of P in terms of t, the radian measure of the angle that segment O-A makes with the positive x axis. The following equalities (which you may assume) will help.

a. x = AQ 

b. y = 2 - AB sin t

c. AB · OA = (AQ)²

Transcribed Image Text:

y = 2 Q y (0, 1) B A P(x, y) X