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}= R^{2}.
Since the circle passes through (2, 7), x=2, y= 7 must satisfy that:
(2a)^{2}+ (7b)^{2}= R^{2}.
Do the same with the other two points and you have 3 equations to solve for the 3 unknowns a, b, and R.
