SOLUTION: Find an equation of a parabola with focus (3,2) and directrix x = 4

Question 327801: Find an equation of a parabola with focus (3,2) and directrix x = 4
Answer by galactus(183) (Show Source): You can put this solution on YOUR website!
This parabola opens to the left. This is because the directrix lies to the right of the focus.
Thus, it has equation of the form
where (h,k) is the coordinates of the vertex.
p is the distance from the vertex to the directrix and from the vertex to the focus. Since the distance from the focus to the directrix for this one is only 1. Then, p=1/2. Note that the distance from the focus to the directrix is 2p.
This means the vertex is only 1/2 units from the focus toward the directrix.
So, h=7/2 and k=2
So, we have

To write it in standard form:

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