Question 546684: Given the focus of the parabola (0,-6), and the directirx y=6, find the equation of the parabola.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Given the focus of the parabola (0,-6), and the directirx y=6, find the equation of the parabola.
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Since the focus is below the directrix on the axis of symmetry,(x=0), this is a parabola which opens downward. Its standard form of equation: (x-h)^2=-4p(y-k), (h,k) being the (x,y) coordinates of the vertex:
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For given parabola:
y-coordinate of vertex=half-way between directrix and focus on axis of symmetry=0
x-coordinate of vertex=0
vertex: (0,0)
p=distance from vertex to focus or to directrix on the axis of symmetry=6
Equation of given parabola:
(x-0)^2=-4p(y-0)
x^2=-24y (ans)
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