Find the equation of the circle which passes through the points (1, 3) and (2, - 1), and has its centre on the line 2x + y – 4 = 0.
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)
Since the centre lies on the given straight line, ( - g, - f) must satisfy the equation as
- 2g –f - 4 = 0…(iv)
Solving, f = - 1, g = - 1.5, c = - 1
The equation is
x2 + y2 - 3x - 2y - 1 = 0