Question

The lines $3x-4y+4=0$ and $6x-8y-7=0$ are tangent to the same circle. The radius of the circle is :

• A. $\frac{1}{2}$
• B. $\frac{3}{4}$
• C. $\frac{3}{2}$
• D. $2$

Answer 1

Answer: (B)

$\frac{3}{4}$

$3x-4y+4=0$ and $3x-4y-\frac{7}{2}=0$ are two parallel tangents of the same circle.
Then perpendicular distance between these parallel lines is equal to diameter of that circle.
$\therefore 2r=\left|\frac{4+\frac{7}{2}}{\sqrt{3^2+4^2}}\right|=\frac{15}{2\times 5}$
$r=\frac{15}{20}=\frac{3}{4}$
$\Rightarrow$ radius of the circle = $\frac{3}{4}$