I have a circle whose center is at point (5,-2) and goes through (1,1)
I can't tell for sure if this passes through (1,1) or not from the wolfram graph but looks pretty close.
Substitute x = 1 and y = 1 into the equation . . . Do they satisfy the equation?
To convert to polar coordinates, I'd do it like this . . .
You can use the Quadratic Formula to solve for . . . but it's pretty ugly!