y24y2x40 write in standard form and sketch find vertexfocus

y²-4y-2x-4=0   

write in standard form and sketch, find vertex,focus and directrix. show all work leading to answers.

Solution

y²-4y -2x-4=0

y²-4y+4-4-2x-4=0

(y-2)² -2x-8=0

x=(1/2)(y-2)²-4

This is of the form

x=a(y-k)²+h

4p=2

p=1/2

Where vertex is (h,k)   that is (-4,2)

focus is(h+p,k) = (-4+1/2 , 2) = (-7/2,2)

directrix, x=h-p

              x= -4-1/2=-9/2