A) a parabola
B) a straight line
C) an ellipse
D) a hyperbola
Correct Answer: A
Solution :
Let the equation of the circle is \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] As it passes through (0, 2b) \[\therefore \]\[4{{b}^{2}}+4fb+c=0\] ...(i) Also, the circle made an intercept on the x-axis \[\therefore \]\[2\sqrt{{{g}^{2}}-c}=4a\Rightarrow c={{g}^{2}}-4{{a}^{2}}\] Substituting this value in (i), we get \[4{{b}^{2}}+4fb+{{g}^{2}}-4{{a}^{2}}=0\] \[\therefore \]Locus of centre is \[{{x}^{2}}+4by+4({{b}^{2}}-{{a}^{2}})=0,\]which is the equation of parabola.
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