A) \[(0,\,\,2)\]
B) \[(1,\,\,2)\]
C) \[(2,\,\,0)\]
D) \[(2,\,\,1)\]
Correct Answer: A
Solution :
Given equation of parabola is \[{{y}^{2}}=4y-4x\] \[\Rightarrow \] \[{{y}^{2}}-4y+4=-4x+4\] \[\Rightarrow \] \[{{(y-2)}^{2}}=-4(x-1)\] \[\Rightarrow \] \[{{Y}^{2}}=-4X\] where\[Y=y-2,\,\,X=x-1\] The coordinates of focus are\[(-1,\,\,0)\]. \[i.e.,\] \[x-1=-1,\,\,y-2=0\] \[\Rightarrow \] \[x=0,\,\,y=2\] \[\therefore \]Required coordinate is\[(0,\,\,2)\].
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