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

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

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

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