First slide

Definition of a circle

Question

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

Easy

A

$\sqrt{5}$
B

$2 \sqrt{5}$
C

$3 \sqrt{5}$
D

$4 \sqrt{5}$

Solution

The normals pass through the centre of the circle
Solving x + y = 6, x + 2y = 4 we get centre
Centre = (8, - 2) = C
(6, 2) = P
$r = C P = \sqrt{4 + 16} = 2 \sqrt{5}$

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