Circle And System Of Circles Question 243
If the equation $ x^{2}+y^{2}+2gx+2fy+c=0 $ represents a circle with x-axis as a diameter and radius a, then the center is at ( -g, -f ) and the radius is $ \sqrt{g^{2}+f^{2}-c} $, so $ \sqrt{g^{2}+f^{2}-c} = a $ and the diameter lies on the x-axis implying f = 0.
Options:
A) $ f=2a,\ g=0,\ c=3a^{2} $
B) $ f=0,\ g=a,\ c=3a^{2} $
C) $ f=0,\ g=-2a,\ c=3a^{2} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Here $ \sqrt{f^{2}+g^{2}-c}=a $
f must be zero;
$ \Rightarrow g^{2}-c=a^{2} $ .
BETA
