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 $\left(\frac{5}{4},1\right)$ .