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

Answer: (B)

If two parallel lines touching the circle, then radius of a circle is half the distance between the tangents. Since, given tangent lines
$3x-4y+5=0$ and $3x-4y-\frac{9}{2}=0$ are parallel.
$\therefore$ Distance between the lines
$=\frac{|a_1-a_2|}{\sqrt{a^2+b^2}}$
$=\frac{|5+\frac{9}{2}|}{\sqrt{9+16}}=\frac{19}{10}$
$\therefore$ Radius $=\frac{1}{2}\times \frac{19}{10}$
$=\frac{19}{20}=0.95$