Find the equation of the circle passing through the points (1,2), (3,-4) and (5,-6)

${x}^{2}+{y}^{2}+2gx+2fy+c=0\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}2g+4f+c+5=0\phantom{\rule{0ex}{0ex}}6g-8f+c+25=0\phantom{\rule{0ex}{0ex}}10g-12f+c+61=0\phantom{\rule{0ex}{0ex}}$

Solving we get

*g*= - 11,

*f*= - 2 and

*c*= 25

Therefore, the required equation is ${x}^{2}+{y}^{2}-22x-4y+25=0$

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