Converting from Rectangular Coordinates to Polar - Problem 2

We're converting equations from rectangular form to polar form. Here is a slightly harder example. X² plus y² minus the square root of x² plus y², minus y equals 0. So let's recall that x² plus y² is r². So this whole thing can be written as r² minus, and then I have the square root of r² minus, and then y is the same as r sine theta. This is just r.

I have r² minus r minus r sine theta equals 0. Now I can factor r out. I get r minus 1, minus sine theta. That tells me that, in order for this equation to be satisfied, either r equals 0, or r equals 1 plus sine theta.

Now it turns out that r equals 0 is redundant. I don't actually need it. What does r equals 0 represent? Well it represents the point at the origin, the pole. So if I can actually get that point from this equation, I don't need this part.

I do get that point when theta equals 3 pi over 2, because one theta equals 3 pi over 2, this equals-1. So I'll get r equals 0 then. So I don't need this part. This is redundant.

My final equation is just this. So it's actually much simpler in polar coordinates, this equation than in rectangular.