Let the required equation of the circle be
` x ^(2) + y ^(2) + 2 gx + 2 fy + c = 0" "` … (i)
Clearly, the circle passes through the point ` O ( 0,0), A(- 2, 0) and B(0, 3)`
Putting ` x = 0 and y = 0 ` in (i), we get c = 0
Thus (i) becomes
` x^(2) + y ^(2) + 2gx + 2 fy = 0 `
Putting ` x = - 2 and y = 0 `in (ii) we get
` 4 g = 4 hArr g = 1 `.
Putting ` x = 0 and y = 3 ` in (iii), we get
` 6f = - 9 hArr f = (-3)/(2)`
Putting ` g = 1 and f = (-3)/(2)` in (ii), we get ` x ^(2) + y ^(2) + 2x - 3y = 0 `
which is the required equation of the circle.
