A) \[{{x}^{2}}+{{y}^{2}}+9x+2fy+14=0\]
B) \[3{{x}^{2}}+3{{y}^{2}}+27x-2fy+42=0\]
C) \[{{x}^{2}}+{{y}^{2}}-9x+2fy+14=0\]
D) \[{{x}^{2}}+{{y}^{2}}-2fy-9y+14=0\]
Correct Answer: C
Solution :
The circle g, f, c passes through (2, 0) \[\therefore \]\[4+4g+c=0\] ?.(i) Intercept on x-axis is \[2\sqrt{({{g}^{2}}-c)}=5\] \[\therefore \ 4({{g}^{2}}+4g+4)=25\] by (i) or \[(2g+9)(2g-1)=0\Rightarrow g=-\frac{9}{2},\ \frac{1}{2}\] Since centre \[(-g,\ -f)\] lies in 1st quadrant, we choose \[g=-\frac{9}{2}\] so that \[-g=\frac{9}{2}\] (positive). \[\therefore \ c=14\], (from (i)).
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