SOLUTION: Find an equation of the parabola that satisfies the given conditions. Focus F(8, 4), directrix y = −2

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Question 813796: Find an equation of the parabola that satisfies the given conditions.
Focus F(8, 4), directrix y = −2
Answer by lwsshak3(11628) About Me  (Show Source):
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Find an equation of the parabola that satisfies the given conditions.
Focus F(8, 4), directrix y = −2.
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Given data show parabola opens upwards.
Its basic form of equation:
%28x-h%29%5E2=4p%28y-k%29, (h,k)=(x,y) coordinates of the vertex, p=distance from vertex to focus and directrix on the axis of symmetry
For given parabola:
axis of symmetry: x=8
x-coordinate of vertex=8
y-coordinate of vertex=(4+(-2))/2=2/2=1 (midpoint between focus and directrix on the axis of symmetry.
Vertex:(8,1)
p=3 (distance from vertex to focus and directrix on the axis of symmetry.
4p=12
equation of given parabola:%28x-8%29%5E2=12%28y-1%29