Question

The focus of the parabola $y^2=4y-4x$ is:

• A. (0, 2)
• B. (1, 2)
• C. (2, 0)
• D. (2, 1)

Answer 1

Answer: (A)

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 $(0,2)$.