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A parabola can be drawn given a focus of (8,4) and a directrix of x = 6. Write the

equation of the parabola in any form.

User NeitoFR
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1 Answer

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Answer:

x = 1/4(y -4)² +7

Explanation:

A parabola can have the equation ...

x = 1/(4p)(y -k)² +h

where the vertex is (h, k), and the vertex-to-focus distance is p.

The vertex is halfway between the focus and directrix, so has coordinates ...

((8, 4) +(6, 4))/2 = (7, 4)

The distance from the vertex to the focus is 8-7 = 1, so the equation can be written ...

x = 1/4(y -4)² +7

A parabola can be drawn given a focus of (8,4) and a directrix of x = 6. Write the-example-1
User Smith John
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