A) \[2\sqrt{3}\]
B) \[3\sqrt{2}\]
C) \[2\sqrt{2}\]
D) \[\sqrt{2}\]
E) \[2\sqrt{5}\]
Correct Answer: E
Solution :
Given equation of parabola, \[y={{x}^{2}}-4x+3\] \[\Rightarrow \] \[(y+1)={{x}^{2}}-4x+4\] \[\Rightarrow \] \[{{(x-2)}^{2}}=(y+1)\] Comparing with, \[{{X}^{2}}=4aY\]here\[X=x-2\]and \[y=y+1,a=\frac{1}{4}\] Vertex is\[(2,-1)=V\](say) equation of circle, \[{{x}^{2}}=9-{{(y-3)}^{2}}\] or \[{{(x-0)}^{2}}+{{(y-3)}^{2}}=9\] Centre \[C=(0,\text{ }3)\] Now, \[VC=\sqrt{{{(2-0)}^{2}}+{{(-1-3)}^{2}}}\] \[=\sqrt{4+16}=\sqrt{20}\] \[=2\sqrt{5}\]
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