Find the equation of the circle passing through the points `(1,-2)a n d(4,-3)` and whose centre lies on the `3x+4y=7.`

Explanation

Let the equation of circle be
`x^(2)+y^(2)+2gx+2gy+c=0`….(1)
This circle passes through the point (1, -2)
`rArr2g-4f+c=-5`….(2)
This circle passes through the point (4, -3)
`16+9+8g -6f +c =0`
`rArr 8g-6f +c =-25` ….(3)
Centre of circle `(-g,-f)`, lies on the line `3x + 4y = 5`
`:. -3g - 4f =5` ....(4)
From eqs. (2),(3) and (4)
`g =-3,f=1,c=5`
Put these value in eq. (1)
`x^(2)+y^(2)-6x+2y+5=0`.