“How do I write the equation of a circle with center (5,-7) and radius 9 units?”

I would write this equation so it’s similar to how the equation of an ellipse would look. The denominators will be the same. And you could write this in different ways, but I think this way clearly shows the center and radius.

Having one on the right side of the equation, shows you the radius in the denominators and would show the major and minor axes if it was an ellipse.