Answer:

The equation of a circle: x² + y² + 2gx + 2fy + c = 0…(i)

Putting (1, 3) & (2, – 1) in (i)

2g + 6f + c = – 10..(ii)

4g – 2f + c = – 5..(iii)

The centre lies on the given straight line, ( – g, – f) must satisfy the equation.

– 2g –f – 4 = 0…(iv)

Solving,

f = – 1, g = – 1.5, c = – 1

The equation is x² + y² – 3x – 2y – 1 = 0