Question

The distance of the point $(1,2)$ from the common chord of the circles $x^2+y^2+6x-16=0$ and $x^2+y^2-2x-6y-6=0$ is

• A. $1$
• B. $\frac{1}{5}$
• C. $5$
• D. $2$

Answer 1

Answer: (A)

$1$

$S_1:x^2+y^2+6x-16=0$

$S_2:x^2+y^2-2x-6y-6=0$

Equation of common chord of $S_1$ and $S_2$ is

$S_1-S_2=0$
$\Rightarrow 8x+6y-10=0$
$\Rightarrow 4x+3y-5=0$

Distance of $(1,2)$ from $4x+3y-5=0$ is
$d=\left|\frac{4+6-5}{5}\right|=1$
Hence, option A.