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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.`

Text Solution

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Let the equation of the circle be
`x^(2)+y^(2)+2gx+2fy+c=0` (1)
If (1) passes through the points (1,-2) and (4,-3), then
`5+2g-4f+c=0` (2)
and `25+8g-6f+c=0 ` (3)
Since the center `(-g,-f)` lies on the line `3x+4y=7`, we have
`-3g-4f=7` (4)
Solving (2), (3), and (4), we get
`g=-(47)/(15),f=(3)/(5)`, and `c=(11)/(3)`
Substituting in (1), the equation of the circle is
`15x^(2)+15y^(2)-94x+18y+55=0`
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