Question 1168585: Find the equation of parabola in standard form having the given properties
a. Vertex at (2,4), focus at (-3,4)
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The vertex form for a vertical parabola is: 4p(y-k) = (x-h)^2, where (h,k) is the vertex. The focus lies at the point (h,k+p). Since the x coordinates of the vertex and focus don't match, the parabola most open sideways.
In that case, the vertex form is 4p(x-h) = (y-k)^2, with vertex (h,k) and focus (h+p,k). h+p = -3 -> p = -3 -2 = -5. Hence the equation becomes (y-4)^2 = -20(x-2).
Put in standard form:
y^2 -8y + 16 = -20x + 40 -> y^2 - 8y - 24 = -20x -> x = -y^2/20 + (2/5)y + 6/5
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