Question

The lines $3x-4y+4=0$ and $6x-8y-7=0$ are tangents to the same circle. Then find the radius of the circle.

Answer 1

$3x-4y+4=0$ and $6x-8y-7=0$ are the $2$ tangents which are parallel. Therefore distance between them is $=$ diameter dis bet $3x-4y+4=0$ & $3x-4x-\frac{7}{2}=0$ is

$\frac{4-\left(\frac{-7}{2}\right)}{\sqrt{9+16}}=\frac{\frac{8+7}{2}}{\sqrt{25}}=\frac{15}{2\times 5}=\frac{3}{2}$

$\therefore$ radius $=\frac{3}{2}/2=\frac{3}{4}$ units