Question

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

• A. $\frac{3}{2}$
• B. $\frac{3}{4}$
• C. $\frac{1}{10}$
• D. $\frac{1}{20}$

Answer 1

The correct option is B $\frac{3}{4}$

$3x-4y+4=0...........\left(i\right)$
$slope=\frac{3}{4}$
$6x-8y-7=0$
$3x-4y-\frac{7}{2}=0........\left(ii\right)$
$slope=\frac{3}{4}$
$\sin cetheslopeof\left(i\right)and\left(ii\right)aresame$
$Hencelinesareparallel$
$Thedis\tan cebetweentwolinesisdiameterofcircle$
$letpbethediameterofcircle$
$d=p=\left|\frac{c_1-c_3}{\sqrt{a^2+b^2}}\right|$
$=\left|\frac{4-\frac{7}{2}}{\sqrt{3^2+4^2}}\right|$
$=\frac{3}{2}$
$radius=\frac{Diameter}{2}$
$=\frac{3}{2}\left(\frac{1}{2}\right)=\frac{3}{4}$