Circle And System Of Circles Question 150
Question: A circle is concentric with the circle $ x^{2}+y^{2}-6x+12y+15=0 $ and has area double of its area. The equation of the circle is
Options:
A) $ x^{2}+y^{2}-6x+12y-15=0 $
B) $ x^{2}+y^{2}-6x+12y+15=0 $
C) $ x^{2}+y^{2}-6x+12y+45=0 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Equation of circle concentric to given circle is $ x^{2}+y^{2}-6x+12y+k=0 $ …………. (i)
Radius of circle (i) $ =\sqrt{2} $ (radius of given circle)
$ \Rightarrow \sqrt{9+36-k}=\sqrt{2}\sqrt{9+36-15} $
$ \Rightarrow 45-k=60\Rightarrow k=-15 $
Hence the required equation of circle is $ x^{2}+y^{2}-6x+12y-15=0 $ .
BETA
