A) \[(1/4,\,\,0)\]
B) \[(1,\,\,2)\]
C) \[(5/4,\,\,1)\]
D) \[(3/4,\,\,5/2)\]
Correct Answer: C
Solution :
Given equation of parabola be \[{{y}^{2}}-x-2y+2=0\] \[\Rightarrow \] \[{{y}^{2}}-2y+1=x-1\] \[\Rightarrow \] \[{{(y-1)}^{2}}=x-1\] \[\Rightarrow \] \[{{Y}^{2}}=X\] where \[Y=y-1,\,\,X=x-1,\,\,a=\frac{1}{4}\] \[\therefore \]Focus is\[(a,\,\,0)\] \[\Rightarrow \] \[x-1=\frac{1}{4},\,\,y-1=0\] \[\Rightarrow \] \[x=\frac{5}{4},\,\,y=1\] \[\therefore \] Required focus is\[\left( \frac{5}{4},\,\,1 \right)\].
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