Consider a circle of radius centered
at , as in the figure. Let a line from
the origin to a point on the circle intersect
the line at . Finally, let
be the point of intersection of a horizontal line through
and a vertical line through . As ,
the angle makes with the positive -axis
varies, point traces out a curve called the
witch of Agnesi.

(a) Find a vector-parametric equation
for the point in terms of the parameter .
Your answer should be of the form and include the angle brackets.

(b) Find a vector-parametric equation
for the point in terms of the parameter .

(c) Find a vector-parametric equation
for the point in terms of the parameter .