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