finding the equation of a circle from given point on the graph
Those are very good geometric ways to specify the circle. Since the original question asked for the equation, you could also do this: the equation of a general circle with center (a,b) and radius R is
(x- a)2+ (y- b)2= R2.
Since the circle passes through (-2, 7), x=-2, y= 7 must satisfy that:
(-2-a)2+ (7-b)2= R2.
Do the same with the other two points and you have 3 equations to solve for the 3 unknowns a, b, and R.