A longbow curve is defined as follows. Draw a circle in the xy-plane with radius a and center
(0, a) and draw the horizontal line y  2a . Each non-horizontal line through the origin intersects the
circle at a point A and the line y  2a at point B. Let P be the midpoint of the segment from A to B.
The set of all points P obtained in this way traces out the longbow curve as the lines through the
origin rotate from   0 to    , where  is the angle the line makes with the positive x axis. Find
a parametrization of this curve in terms of the angle  .
B
P
A
MVC