Circle And System Of Circles Question 65
Question: A circle $ x^{2}+y^{2}+2gx+2fy+c=0 $ passing through $ (4,\ -2) $ is concentric to the circle $ x^{2}+y^{2}-2x+4y+20=0 $ , then the value of c will be
[RPET 1984, 86]
Options:
A) - 4
B) 4
C) 0
D) 1
Show Answer
Answer:
Correct Answer: A
Solution:
Circle $ x^{2}+y^{2}+2gx+2fy+c=0 $ is concentric with $ x^{2}+y^{2}-2x+4y+20=0 $ . Therefore centre is $ (1,\ -2) $ and radius $ =\sqrt{g^{2}+f^{2}-c}=\sqrt{{{(1-4)}^{2}}+{{(-2+2)}^{2}}} $
$ \Rightarrow c=-4 $ .
BETA
