(552, #31) Find parametric equations for the set of all points
P determined as shown in the figure, using the angle theta
as the parameter. Then eliminate the parameter and identify the curve.
Solution :
Looking at the figure we see that
.
So the parametric equations are
and .
From the identity we get the equation
.
Thus our curve is the equation which
is an ellipse.
.
and 
.
we get the equation
.
which
is an ellipse.