Question

The perpendicular distance of radical axis determind by the circles
$x^2+y^2+2x+4y-7=0$ and $x^2+y^2-6x+2y-5=0$ from the origin is

• A. $\frac{1}{\sqrt{17}}$
• B. $\frac{1}{4}$
• C. $\frac{1}{5}$
• D. $\frac{2}{17}$

Answer 1

The correct option is A $\frac{1}{\sqrt{17}}$

Radical axis can be found as

$x^2+y^2+2x+4y-7-(x^2+y^2-6x+2y-5)=0⟹8x+2y-2=0$

Perpendicular distance from origin $=\Vert \frac{-2}{\sqrt{8^2+2^2}}\Vert =\frac{1}{\sqrt{17}}$

This is the required solution.