Question

If the lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are two parallel tangents to a circle, then the length of its diameter is _____________.

Answer 1

Given two parallel tangents 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0
$\mathrm{i}.\mathrm{e}.3x-4y-\frac{7}{2}=0$
Distance between these two parallel tangents is $\frac{\left|4+{\displaystyle \frac{7}{2}}\right|}{\sqrt{9+16}}$

$=\frac{\left|8+7\right|}{2\times 5}$

i.e distance between parallel tangents$=\frac{15}{10}=\frac{3}{2}$ .