Mathematics - Circle Question with Solution | TestHub

Let the two circles be $x^2+y^2+2g_{1}x+2f_{1}y$ $+c_1=0$ and $x^2+y^2+2g_{2}x+2f_{2}y+c_2=0$ where $g_1=5/2,f_1=3/2,c_1=7,g_2=4,f_2=3$ and ${\mathrm{c}}_2=\mathrm{k}$ If the two circles intersects orthogonally, then $\begin{array}{rl}& 2\left({\mathrm{g}}_1{\mathrm{g}}_2+{\mathrm{f}}_1{\mathrm{f}}_2\right)={\mathrm{c}}_1+{\mathrm{c}}_2\Rightarrow 2\left(-10+\frac{9}{2}\right)=7+\mathrm{k}\\ & \Rightarrow 11=7+\mathrm{k}\Rightarrow \mathrm{k}=-18\end{array}$