SOLUTION: I have such a hard time doing this problem: Write Standard Equation of Parabola, Given Focus: (-2,3)and Directrix: x=2.

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Question 170164: I have such a hard time doing this problem: Write Standard Equation of Parabola, Given Focus: (-2,3)and Directrix: x=2.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
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

So the x-coordinate of the vertex is . This means that

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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 . This means that

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

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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

Start with the standard equation (for parabolas that open up to the left)

Plug in , , and

Multiply

So the standard equation is