A) \[(1,\,\,1)\]
B) \[(1,\,\,0)\]
C) \[(1,\,\,-1)\]
D) \[(0,\,\,0)\]
Correct Answer: A
Solution :
Given, parabola is\[y={{x}^{2}}\] ... (i) and straight line\[y=2x-4\] ... (ii) From Eqs. (i) and (ii),\[{{x}^{2}}-2x+4=0\] Let \[f(x)={{x}^{2}}-2x+4\] On differentiating w.r.t.\[x,\] we get \[f'(x)=2x-2\] For least distance,\[f'(x)=0\] \[\Rightarrow \] \[2x-2=0\] \[\Rightarrow \] \[x=1\] On putting \[x=1\] in Eq. (i), we get \[y=1\] Hence, the point least distance from the line is\[(1,\,\,1)\].
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