First slide

Definition of a circle

Question

The radius of the circle touching the straight lines $x - 2 y - 1 = 0$ and $3 x - 6 y + 7 = 0$ is

Easy

A

$\frac{1}{\sqrt{2}}$
B

$\frac{\sqrt{5}}{3}$
C

$\sqrt{3}$
D

$\sqrt{5}$

Solution

Given lines are parallel to each other
$∴$ distance between the parallel lines = diameter of the circle

$∴$ radius $= \frac{d i s t a n c e b e t w e e n t h e p a r a l l e l l i n e s}{2}$

$= \frac{1}{2} . \frac{| \frac{7}{3} + 1 |}{\sqrt{(1 + 4)}} = \frac{\sqrt{5}}{3}$

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