Two circles centered at $(2,3)$ and $(4,5)$ intersects each other. If their radii are equal, then the…
Two circles centered at $(2,3)$ and $(4,5)$ intersects each other. If their radii are equal, then the equation of the common chord is
$x+y+1=0$
$x+y-1=0$
$x+y-7=0$
$x+y+7=0$
Solution
Equation of common chord is $S_1-S_2=0$, where $S_1$ and $S_2$ are equations of the circles
$\begin{aligned}
& \therefore\left[(\mathrm{x}-2)^2+(\mathrm{y}-3)^2\right]-\left[(\mathrm{x}-4)^2+(\mathrm{y}-5)^2\right]=0 \\
& \therefore-4 \mathrm{x}+4-6 \mathrm{y}+9+8 \mathrm{x}-16+10 \mathrm{y}-25=0 \\
& \therefore 4 \mathrm{x}+4 \mathrm{y}-28=0 \quad \Rightarrow \mathrm{x}+\mathrm{y}=7
\end{aligned}$