Hm;; I don't end up with a negative number;; I get a positive number on the right side.

(3r2x-(54/3r2)))^2+(2y+4)^2= (6r2)^2 => this is basically ()^2 + ()^2= ()^2

the key part is that there is + in between, so I guess not hyperbola. If you look up on the end of chapter summary or first cover you will see something with a similar format.

I feel like this is a circle but I could be totally wrong.