Question

The radius of the circle passing through the point (6, 2) and two of whose diameters are x + y = 6 and x + 2y = 4 is

• A. 4
• B. 6
• C. 20
• D. $\sqrt{20}$

Answer 1

The correct option is D $\sqrt{20}$

Given, diameters of the circles are x + y = 6 and x + 2y = 4. We know that the intersection point of the diameters is called centre of the circle.
$\therefore$ Centre (8, -2)

Since the circle is passing through the point (6, 2) Hence the distance between the centre (8, – 2) and point (6, 2) will be the radius of the circle.

$\therefore$ Radius of the circle

$=\sqrt{(6-8{)}^2+(2+2{)}^2}=\sqrt{4+16}=\sqrt{20}.$