The equation used is the standard equation that has the form: (x - h) ^ 2 + (y - k) ^ 2 = r ^ 2. where h and k are the x and y coordinates of the center of the circle and r is the radius. Substituting values: (x - 2) ^ 2 + (y + 5) ^ 2 = 6 ^ 2. We substitute the point (m, -5) in the equation of the circumference: (m - 2) ^ 2 + (-5 + 5) ^ 2 = 6 ^ 2. Rewriting: (m - 2) ^ 2 + 0 = 6 ^ 2 (m - 2) ^ 2 = 6 ^ 2 (m - 2) = 6 m = 6 + 2 m = 8 Answer: the value of m is: m = 8
