this version of the question.
I'm following this approach.
If the center is (-g,-f )and the equation x^2 + y^2 +2gx +2fy +c =0.
here the radius is equal to g.
and c =f^2
For the given two points the value of radius will be equal (distance of the center and two points).
The value of g=5, and so radius = 5.
But the value of f does not come according to the answer, it becomes a complex number.