Question

if (-4,-2) and (2,6) are opposite points on a circle, what is the equation of the circle?

Answer 1

The center is the midpoint of these two points, so is ((-4+2)/2, (-2+6)/2) = (-1, 2). The radius is the distance from the center to either of these points. Its square is 3^2 +4^2 = 25.

The equation of the circle is
.. (x +1)^2 +(y -2)^2 = 25