A) a parabola
B) a circle
C) an ellipse
D) a hyperbola
Correct Answer: A
Solution :
Let the centre of a circle be\[{{C}_{1}}(h,\,\,k)\] Since, \[{{C}_{1}}{{C}_{2}}={{r}_{1}}+{{r}_{2}}\] (given) \[\Rightarrow \] \[\sqrt{{{(h-0)}^{2}}+{{(k-3)}^{2}}}=|k+2|\] \[\Rightarrow \] \[{{h}^{2}}=5(2k-1)\] Hence, locus of a point is\[{{x}^{2}}=5(2y-1)\]which represents\[\text{a}\]equation of parabola.
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