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Q.
If the length of the common chord of two circles $x^{2}+y^{2} +8 x+1=0$ and $x^{2}+y^{2}+2 \mu y-1=0$ is $2 \sqrt{6}$, then the values of $\mu$ are
Conic Sections
Solution:
The common chord is $S_{1}-S_{2}=0$.
$ 4 x-\mu y+1=0$
$\therefore A C=$ Radius of first circle $=\sqrt{15}$
$ A M=\frac{A B}{2}=\sqrt{6} $
$ \therefore C M=3 $
$\therefore \frac{|-16+1|}{\sqrt{16+\mu^{2}}}=3$
or $ \mu=\pm 3$
