Question

For the circles $S_1=x^2+y^2-4x-6y-12=0$ and $S_2=x^2+y^2+6x+4y-12=0$ and the line $L\equiv x+y=0$

• A. $L$ is common tangent of $S_1$ and $S_2$
• B. $L$ is common chord of $S_1$ and $S_2$
• C. $L$ is radical axis of $S_1$ and $S_2$
• D. $L$ is perpendicular to the line joining the centre of $S_1$ and $S_2$

Answer 1

Answer: (B), (C), (D)

$L$ is common chord of $S_1$ and $S_2$
$L$ is perpendicular to the line joining the centre of $S_1$ and $S_2$
$L$ is radical axis of $S_1$ and $S_2$

Clearly line $L$ is radical axis of of the given pair of circle.
And we know radical axis is perpendicular to the line joining the centre of the circles.
Also $C_1{C}_2<r_1+r_2$. So both the circles intersect at two point.
Thus line $L$ is also common chord.