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directrix y=9−x2
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Solution
y=374
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Parabola Directrix
A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (the directrix)
Parabola standard equation
4p(y−k)=(x−h)2 is the standard equation for an up-down facing parabola with vertex at (h,k), and a focal length |p|
Rewrite y=9−x2in the standard form:4(−14)(y−9)=(x−0)2
(h,k)=(0,9),p=−14
Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance −p from the center (0,9) y-coordinate
