You're given 3 points (x, y) on the circle with equation
x ² + y ² + Dx + Ey + F = 0
and you have to use these known points on set up 3 equations involving D, E, and F.
For the point (3, -1), this means when x = 3, y = -1, so
3² + (-1)² + 3D - E + F = 0
→ 3D + (-1)E + 1F = -10
The next point (-2, 4) gives
(-2)² + 4² - 2D + 4E + F = 0
→ (-2)D + 4E + 1F = -20
And from the last point (6, 8),
6² + 8² + 6D + 8E + F = 0
→ 6D + 8E + 1F = -100