Circle And System Of Circles Question 214
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
[Karnataka CET 2004]
Options:
A) 4
B) 6
C) 20
D) $ \sqrt{20} $
Show Answer
Answer:
Correct Answer: D
Solution:
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 $ \equiv (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} $ .
BETA
