We need to find the distance between (-6, 7) and (4, -2) . That distance is the radius of this circle.
distance \(=\sqrt{[(-6)-(4)]^2+[(7)-(-2)]^2} \\~\\ =\sqrt{[10]^2+[9]^2} \\~\\ =\sqrt{100+81} \\~\\=\sqrt{181}\)
So...the radius of this circle is \( \sqrt{181} \) , and the center of this circle is (-6, 7) .
This makes the equation:
( y - 7 )2 + ( x - (-6) )2 = ( \( \sqrt{181} \) )2
( y - 7 )2 + ( x + 6 )2 = 181
