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Question 544860: What is the equation for a parabola in which the set of all points in the plane are equidistant from the focus and line. F(0, -5); y=5
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What is the equation for a parabola in which the set of all points in the plane are equidistant from the focus and line. F(0, -5); y=5
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What you have here is the definition of a parabola.
Axis of symmetry: x=0 or y-axis
Since y-coordinate of focus(-5) is below the directrix(y=5), parabola opens downward.
Standard form of equation for this parabola: (x-h)^2=-4p(y-k), with (h,k)=(x,y) coordinates of the vertex.
x-coordinate of vertex=x-coordinate of focus=0
y-coordinate of vertex=midway between y-coordinate of focus and directrix on the axis of symmetry=0
vertex: (0,0)
p=distance from vertex to focus or directrix on the axis of symmetry=5
4p=20
Equation of given parabola:
(x-h)^2=-4p(y-k)
(x-0)^2=-20(y-0)
x^2=-20y
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