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Question 350003: what is the equation of the parabola who has a focus of (3,-5) and the equation of the directrix is y=-2?
Answer by alanc(27)   (Show Source):
You can put this solution on YOUR website! Refer to the standard form for a parabola: (x-h)^2 = 4a*(y-k) vertex of parabola is at (h,k) focus is at (h, k + a).
directrix at y= k - a
we have y = -2 = k - a and -5 = k + a, with h = 3
-2 = k - a
-5 = k + a
-7 = 2k
k = -7/2
vertex at (3, -7/2)
a = -5 - k = -5 - (-7/2) = -3/2
equation is : (x -3)^2 = 4*(-3/2)*(y - (-7/2))
Equation: (x-3)^2 = -6(y + 7/2)
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