Find the vertex focus and directrix Find the vertex focus an

Find the vertex, focus and directrix:

Find the vertex, focus and directrix: y^2 - 10 y - 27 x + 133 = 0

Solution

y²-10y-27x+133=0

27x=y²-10y +133

27x=y²-10y + 25-25+133

27x=(y-5)²+108

x=(1/27)(y-5)^2 +4

vertex is (4,5)

focus (h+1/4a,k)=(4+27/4,5)=(43/4,5)

directrix , x=h-1/4a= 4-27/4=-11/4