u/Intrepid-Ad1191

Hey y'all! I'm student teaching in a geometry class right now and am teaching equations of circles for the first time. My mentor teacher is great, but also has a history degree rather than a math degree, so he does not always have the attention to detail with teaching math that I personally like to attend to, so I figured I'd reach out here.

I am struggling with distinguishing between how to describe the "forms" for the equation of a circle. I want students to be comfortable converting between the following two forms:

x^(2)+y^(2)+ax+by+c=0

and

(x-h)^(2)+(y-k)^(2)=r^(2)

What do you call these two forms to distinguish between them? I am seeing inconsistency in online resources, so I am curious what terms other teachers use.