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Question 877244: Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = -1
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = -1
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vertex is mid-way between the focus and directrix:
vertex: (-5,2)
standard form of a vertical parabola
(x – h)^2 = 4p(y – k)
(x – (-5))^2 = 4p(y – 2)
(x + 5)^2 = 4p(y – 2)
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p is the distance between the vertex and either the focus or directrix:
p = 3
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so our final equation is:
(x + 5)^2 = 4*3(y – 2)
(x + 5)^2 = 12(y – 2)
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