The radical axis of the co-axial system of circles with limiting points $(1,2)$ and $(-2,1)$ is

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Aicharya · Accepted Answer

The radical axis of the co-axial system of circles with limiting points $A(1,2)$ and $B(-2,1)$ is the perpendicular bisector of line joining limiting points $A$ and $B$. $\because$ Mid-point of $A$ and $B$ is $\left(-\frac{1}{2}, \frac{3}{2}\right)$ and slope of perpendicular to $A B$ is -3 $\therefore$ Equation of required radical axis is $\begin{aligned} & y-\frac{3}{2}=-3\left(x+\frac{1}{2}\right) \ \Rightarrow & y-\frac{3}{2}=-3 x-\frac{3}{2} \ \Rightarrow & 3 x+y =0 \end{aligned}$ Hence, option (d) is correct.

The radical axis of the co-axial system of circles with limiting points \((1,2)\) and \((-2,1)\) is

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