Question 1091307

1.

{{{(x-h)^2= 4p(y-k)}}}  is the standard equation for an up-down facing parabola 

you have

{{{x^2=-4y}}} or

{{{(x-0)^2= 4p(y-0) }}}

vertex is at: ({{{0}}},{{{0}}})

{{{4p=-4}}} =>{{{ p=-1}}}
focus: ({{{0}}}, {{{-1}}})

directrix is above vertex p units:  {{{y = 1}}}

2.
{{{3y^2 = 24x}}}
{{{y^2 = 8x }}}-> {{{(y-0)^2= 4p(x-0)}}}

{{{4p=8}}}->{{{p=2}}}
vertex is at: ({{{0}}},{{{0}}})
focus:({{{2}}}, {{{0}}})

directrix:{{{x = -2}}}


3.
{{{(y + 5/2)^2 = -5(x - 2/9)}}} -> {{{(y-k)^2= 4p(x-h)}}}
->{{{h=2/9}}}, {{{k=-5/2}}}

{{{4p=-5}}}->{{{p=-5/4}}}

vertex: ({{{2/9}}}, {{{-5/2}}})
focus: ({{{2/9-5/4}}}, {{{-5/2}}})=({{{-37/36}}}, {{{-5/2}}})

directrix:{{{ x =2/9+5/4= 53/36}}}