Write the equation of a parabola
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HINT: It helps to sketch a graph to make it clear where the parabola is in relation to the directrix and focus.

The vertex is midway between the directrix (y=8) and the focus (9,-2), so the vertex is (9,(8+(-2))/2)=(9,3). The parabola is inverted because the directrix is above the focus. 

Plugging in the vertex: 4f(y-3)=-(x-9)2, where f is the focal length=3-(-2)=5, so 20y=-x2, or y=-(x-9)2/20+3.

We can tidy this up a bit:

20y=-(x2-18x+81)+60=-x2+18x-81+60=-x2+18x-21,

y=(-x2+18x-21)/20 is the equation of the parabola.

by Top Rated User (1.1m points)

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