Find the Parabola with Focus (2,4) and Directrix y=8 (2,4) , y=8

Math
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Since the directrix is vertical, use the equation of a parabola that opens up or down.
Find the vertex.
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The vertex is halfway between the directrix and focus. Find the coordinate of the vertex using the formula . The coordinate will be the same as the coordinate of the focus.
Simplify the vertex.
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Cancel the common factor of and .
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Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Add and .
Find the distance from the focus to the vertex.
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The distance from the focus to the vertex and from the vertex to the directrix is . Subtract the coordinate of the vertex from the coordinate of the focus to find .
Subtract from .
Substitute in the known values for the variables into the equation .
Simplify.
Find the Parabola with Focus (2,4) and Directrix y=8 (2,4) , y=8

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