10th grade geometry

Quote:

what is the equation to find a circle on a graph based on a minimum of two points

There are 3 parameters to any circle. It's center coordinate, (x0, y0) and it's radius. There are an infinite number of circles passing through 2 points.

In general, I would agree with Rom's answer..... unless the two points were the endpoints of a diameter.. Only one circle could pass through these, because the midpoint of a line connecting the two points would be the center, and the distance from this midpoint to each of the points would be the same, i.e., the radius. Any other circles passing through the two points would be have to be congruent ones with the same center and radius.

I believe I'm correct on this, but any critique of my logic would be welcome!!!

While you're technically correct, the problem doesn't allow you to specify anything like that as stated. It simply says find a circle given two points lying on it.