Formally, to convert from rectangular to polar what you need to do is set and .Originally Posted by telefl89
So, given we get .
Thus, your polar equation is .
Converting from polar to rectangular can be a tad messier. Using the transformations and we can solve for r and :
So, becomes .
What is ? Remember, the argument of cos[ ] is just an angle. Call it . is just the angle such that . What is the cosine of this angle? Well, it's just . So .
Your equation now reads: . There's a bit of simplifying left to do, but it isn't hard, just busy. (Hint: You can't really come up with a "clean" solution for y, so put it in the form of a general conic section: . I found that it fits the form for an ellipse.)