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Find the equation of the circle which pa...

Find the equation of the circle which passes through the points `(1,-2),(4,-3)` and whose center lies on the line `3x+4y=7.`

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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`.
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