Our goal is to show the connection between a given polar equation and the rectangular form of the same equation. Our polar equation is
We begin by looking at the graph to determine its center and lengths of the major and minor axes.
We see that the center of the ellipse is (3,0) is rectangular form. The length of the major axis is 10 and the length of the minor axis is 8. From this information, we can write the equation of the ellipse in rectangular form:
Now the important step is to prove that these equations are indeed the same. To begin, remember that
and
and 
We take the following steps
YES! They are equivalent equations, one
polar and one rectangular.