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Question 823776: Find an equation of a parabola with focus(0,-7) and directrix x = 7
Thanks so much in advance:)
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
given:
focus(0,-7)
directrix x = 7
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directrix is a vertical line, so parabola is horizontal.
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find vertex, half way between focus and directrix:
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h = (7 - 0)/2 + 0
h = 7/2 = 3.5
vertex = (h,k) = (3.5, -7)
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directrix is to the right of the focus so parabola opens to the left and p is negative
distance between focus and vertex: p = -3.5
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conic form of horizontal parabola:
4p(x – h) = (y – k)^2
4(-3.5)(x – 3.5) = (y + 7)^2
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answer:
-14(x – 3.5) = (y + 7)^2
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