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  4. The focus of the parabola y2=4 y-4 x is:

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Q. The focus of the parabola $y^{2}=4 y-4 x$ is:

Jharkhand CECEJharkhand CECE 2003

Solution:

Given equation of parabola is $y^{2}=4 y-4 x$
$ \Rightarrow y^{2}-4 y+4=-4 x+4 $
$\Rightarrow(y-2)^{2}=-4(x-1)$
$ \Rightarrow Y^{2}=-4 X$
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 $(0,2)$.