Question

The radius of any circle touching the lines $3x-4y+5=0$ and $6x-8y-9=0$ is

• A. $\frac{19}{10}$
• B. $\frac{19}{20}$
• C. $\frac{9}{20}$
• D. $\frac{90}{20}$

Answer 1

The correct option is B $\frac{19}{20}$

$3x-4y+5=0$ and $3x-4y-\frac{9}{2}=0$ are two parallel tangents of circle.
So, perpendicular distance between these two lines is equal to diameter of circle.
$\therefore 2r=\left|\frac{5+\frac{9}{2}}{\sqrt{3^2+4^2}}\right|$
$2r=\frac{29}{2\times 5}$
$\Rightarrow r=\frac{19}{20}$
Radius of circle is $\frac{19}{20}$.