Question

The focus of the parabola $ y^{2}-x-2y+2=0 $ is:

• A. $ (1/4,\,0) $
• B. $ (1,\, 2) $
• C. $ (5/4,\,1) $
• D. $ (3/4,\,5/2) $

Answer 1

Answer: (C)

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) $ .