Question

The radius of the circle passing through $(6,2)$ and the equation of two normals for the circle are $x+y=6$ and $x+2y=4$ is

• A. $\sqrt{5}$
• B. $2\sqrt{5}$
• C. $3\sqrt{5}$
• D. $4\sqrt{5}$

Answer 1

The correct option is B $2\sqrt{5}$

Normal of a circle passes through its centre.

$x+2y=4$

$x+y=6$

$(-)(-)(-)$

$\_\_\_\_\_\_\_\_\_\_$

$\Rightarrow y=-2$

$x-2=c$

$\Rightarrow x=8$

$\therefore centreofcircle=(8,-2)$

$\therefore$ radius of circle $={\sqrt{(8-6)}}^2+{(-2-2)}^2$

$=\sqrt{4+16}$

$=\sqrt{20}$

$=2\sqrt{5}$Ans.