Question

If the length of the common chord of two circles $x^2+y^2+8x+1=0$ and $x^2+y^2+2\mu y-1=0$ is $2\sqrt{6}$, then the values of $\mu$ are

• A. $\pm 2$
• B. $\pm 3$
• C. $\pm 4$
• D. none of these

Answer 1

Answer: (B)

The common chord is $S_1-S_2=0$.
$4x-\mu y+1=0$
$\therefore AC=$ Radius of first circle $=\sqrt{15}$

$AM=\frac{AB}{2}=\sqrt{6}$
$\therefore CM=3$
$\therefore \frac{|-16+1|}{\sqrt{16+{\mu }^2}}=3$
or $\mu =\pm 3$