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.`

Explanation

Let the equation of circle be `x^2+y^2+2gx+2fy+c=0`

Centre of circle is `(−g,−f)`.

Centre lies on the line `3x+4y=7`

Therefore,
`−3g−4f=7,
3g+4f+7=0 ------- (1)`

Circle passes through the points `(1,-2)` and `(4,-3)`.

By putting these values in the equation of circle,

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