Question 1020336
Complete the square to get into vertex form,
{{{x^2+8x-18=6y}}}
{{{x^2+8x+16-18=6y+16}}}
{{{(x+4)^2-34=6y}}}
{{{y=(x+4)^2/6-34/6}}}
{{{y=(x+4)^2/6-17/3}}}
Vertex is ({{{-4}}},{{{-17/3}}})
The axis of symmetry is {{{x=-4}}}
Switch to focus form,
{{{(x+4)^2=6y+34}}}
{{{(x+4)^2=6(y+17/3)}}}
So then the focus is,
(h,k+p) where {{{p=6}}}.
({{{-4}}},{{{-17/3+18/3}}})
({{{-4}}},{{{1/3}}})
The directrix is then,
{{{y=k-p}}}
{{{y=-17/3-18/3}}}
{{{y=-35/3}}}
*[illustration cf17.JPG].