Question

Write the standard equation for the circle that passes through the points:

(1, 7)

(8, 6)

(7, -1)

Answer 1

there exists a unique circle which passes through these three points.
let the center of the circle be C(h,k). C(the center) is equidistant from all the three given points.
(h-1)^2 + (k-7)^2 = (h-8)^2 + (k-6)^2
by this, we get a linear equation in terms of h and k. Manage to frame one more equation from the above points and solve for h and k
once you get the centre of the circle, you can find the radius and hence the equation of the circle.