Question

If the lines $3x-4y+4=0$ and $6x-8y-7=0$ are tangents to a circle, then the diameter of the circle

• A. $\frac{3}{2}$
• B. $3$
• C. $\frac{5}{2}$
• D. $5$

Answer 1

The correct option is A $\frac{3}{2}$

$3x-4y+4=0$

$3x-4y-\frac{7}{2}=0$

diameter of circle $=\frac{\left|4+\frac{7}{2}\right|}{\sqrt{9+16}}=\frac{15}{2\times 5}=\frac{3}{2}$

Hence,

option $\left(A\right)$ is correct answer.