Circle And System Of Circles Question 87

Question: If the circle $ x^{2}+y^{2}+2gx+2fy+c=0 $ touches x-axis, then

Options:

A) $ g=f $

B) $ g^{2}=c $

C) $ f^{2}=c $

D) $ g^{2}+f^{2}=c $

Show Answer

Answer:

Correct Answer: B

Solution:

Touches x-axis,

Hence radius = ordinate of centre.

Hence $ \sqrt{g^{2}+f^{2}-c}=(-f) $ or $ g^{2}=c $ .