Hint: the point of intersection of the perpendicular bisectors is the center of the circle. Write the equations for the bisectors and solve for the point of intersection. Use the distance from any point to the center to get the radius and, from that, the circle's equation.
I gave you a method. Now you do the work.
Conic sections
A circle passes through points A(-5,2), B(-3,-4) and C(1,8). Find the coordinate of the point of intersection of the perpendicular bisectors of AB and BC. What is the equation of the circle?
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