A) \[c>0\]
B) \[c<0\]
C) \[c=0\]
D) \[c\le 0\]
Correct Answer: B
Solution :
[b] For a circle to meet x-axis in two points on the opposite side of the origin its radius r, should be more the distance of its centre from the origin. Co-ordinate of centre of the circle \[{{x}^{2}}+{{y}^{2}}+2gx\] \[+2fy+c=0\] is \[(-g,-f):\] In the figure shown, \[OQ=OP=r,\] and distance of centre C, from origin, O is CO \[r>\sqrt{OC}\] i.e. \[r>\sqrt{{{(-g)}^{2}}+{{(-f)}^{2}}}\] or \[\sqrt{{{(-g)}^{2}}+{{(-f)}^{2}}-c}>\sqrt{{{(-g)}^{2}}+{{(-f)}^{2}}}\] or, \[{{g}^{2}}+{{f}^{2}}-c>{{g}^{2}}+{{f}^{2}}\] or, \[-c>0\] or, \[c<0\]You need to login to perform this action.
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