Question

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

• A. $1.9$
• B. $0.95$
• C. $2.9$
• D. $1.45$

Answer 1

The correct option is B $0.95$

Given lines $3x-4y+5=0$ and $3x-4y-\frac{9}{2}=0$
which are parallel to each others
$\therefore$ Perpendicular distance
$d=\left|\frac{5+\frac{9}{2}}{\sqrt{3^2+4^2}}\right|=\frac{19}{10}$
$\therefore$ Radius of circle $=\frac{d}{2}=\frac{19}{20}=0.95$