Question

Find the vertex, axis, latus rectum, and focus of the parabolas $y^2=4y-4x.$.

Answer 1

given eqn can be written as
$y^2-4y+4=-4x+4$
$(y-2{)}^2=-4(x-1)$
vertex
$y-2=0$
$\Rightarrow y=2$
$x-1=0$
$\Rightarrow x=1$
vertex (1 , 2)
axis
Y = 2
latus rectum (L.R)
a = -1
L.R = $\left|4a\right|$ = 4
Focus (F)
$x-1=a=-1$
$\Rightarrow x=0$
$y-2=$
$\Rightarrow y=2$
F(0 , 2)