Rewriting a Polar Equation in Rectangular Form

by Amy Benson

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.