25. Equation of the circle cutting orthology the three circles $x^2+y^2-2x+3y-7 = 0, x^2+y^2+5x-5y+9 = 0 and x^2+y^2+7x-9y+29 = 0is$?

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{If} \mathrm{circles} {\mathrm{x}}^2+{\mathrm{y}}^2+2{\mathrm{g}}_1\mathrm{x}+2{\mathrm{f}}_1\mathrm{y}+{\mathrm{c}}_1=0 \mathrm{and} \\ {\mathrm{x}}^2+{\mathrm{y}}^2+2{\mathrm{g}}_2\mathrm{x}+2{\mathrm{f}}_2\mathrm{y}+{\mathrm{c}}_2=0 \mathrm{intersect} \mathrm{orthogonally} \mathrm{then} \\ 2{\mathrm{g}}_1{\mathrm{g}}_2+2{\mathrm{f}}_1{\mathrm{f}}_2={\mathrm{c}}_1+{\mathrm{c}}_2 \\ \mathrm{Let} \mathrm{equation} \mathrm{of} \mathrm{circle} \mathrm{be} \end{gathered}$$



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