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{\left| 5+\frac{9}{2} \right|}{\sqrt{9+16}}=\frac{19}{10} $
$ \therefore $ Radius $ =\frac{1}{2}\times \frac{19}{10} $
$ =\frac{19}{20}=0.95 $