Thread: Polar Coordinates

Hi. I need to figure out how to convert the polar equation

to cartesian coordinates and then graph the resulting equation.

I know it's an ellipse and I know , and , but I can't quite figure out how to make this equation into the standard form for an ellipse. The closest I've come is , which doesn't make any sense. Could someone help me? (Also, I wasn't sure whether this belonged in the calculus or geometry forum, but it's for my calc class so I posted it here.)

First, multiply both sides of your polar equation by r:

Now, use , , and , like you said, to get:

Rearranging:

Completing the square on both the x and y terms:


You should be able to recognise what sort of conic section this is, and be able to graph it.

--Kevin C.

Originally Posted by TwistedOne151

First, multiply both sides of your polar equation by r:

Now, use , , and , like you said, to get:

Rearranging:

Completing the square on both the x and y terms:


You should be able to recognise what sort of conic section this is, and be able to graph it.

--Kevin C.

Thank you Kevin. I always forget to complete the square.