Question 170164
First we need to find the vertex:


X-coordinate of the vertex: Simply average the x coordinate of the focus (-2) with the directix (2) to get {{{(-2+2)/2=0/2=0}}}


So the x-coordinate of the vertex is {{{x=0}}}. This means that {{{h=0}}}


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Y-coordinate of the vertex: This value is equal to the y-coordinate of the focus. So the y-coordinate of the vertex is {{{y=3}}}. This means that {{{k=3}}}



So the vertex is (0,3)



Now that we have the vertex, we can use that to find the distance from the focus to the vertex.


Since the focus (-2,3) is 2 units from the vertex (0,3), this means that {{{p=2}}}


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Now let's find the equation:


Since the focus is (-2,3) and the directrix is x=2, this means that the parabola is opening to the left like this




<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/parabola.png" alt="Photobucket - Video and Image Hosting">



{{{-4p(x-h)=(y-k)^2}}} Start with the standard equation (for parabolas that open up to the left)



{{{-4(2)(x-0)=(y-3)^2}}} Plug in {{{p=2}}}, {{{h=0}}}, and {{{k=3}}}



{{{-8(x-0)=(y-3)^2}}} Multiply



So the standard equation is {{{-8(x-0)=(y-3)^2}}}