A right triangle is shown in the graph. Part A: Use the Pythagorean Theorem to derive the standard equation of the circle, with center at (f, g) and a point on the circle at (x, y). Show all necessary math work.

Part B: If (f, g) = (3, –1) and h = 8, determine the domain and range of the circle.

Part C: Is the point (10, –4) inside the border of the circle if (f, g) = (3, –1) and h = 8? Explain using mathematical evidence.