Q92 / 160 · TS EAMCET 2024 (09 May Shift 2) · Mathematics
Length of the common chord of the circles $x^2+y^2-6 x+5=$ and $x^2+y^2+4 y-5=0$ is
- A$\sqrt{13}$
- Correct answerB$\frac{12}{\sqrt{13}}$
- C$\frac{6}{\sqrt{13}}$
- D$2 \sqrt{13}$
Solution
$x^2+y^2-6 x+5$ and $x^2+y^2+4 y-5=0$
$\begin{aligned}
& \Rightarrow(x-3)^2+y^2=4 \text { and } x^2+(y+2)^2=9 \\
& \Rightarrow a=3, b=-2
\end{aligned}$
Length of common chord $=\left|\frac{2 a b}{\sqrt{a^2+b^2}}\right|=\frac{12}{\sqrt{13}}$.
Hence, the correct answer is option: 'B'.