What is the equation in standard form of the parabola with a focus at (21,15) and a directrix of y= -6?

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What is the equation in standard form of the parabola with a focus at (21,15) and a directrix of y= -6?

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Answer 1 · 2018-06-15T07:09:29

${(x - 21)}^{2} = 42 (y - 4.5)$ $(x-21)^2=42(y-4.5)$

Explanation:

Given -

Focus $(21, 15)$ $(21, 15)$
Directrix $y = - 6$ $y=-6$

This parabola opens up. Its origin is away from the origin $(h, k)$ $(h, k)$ .

Where -

$h = 21$ $h=21$
$k = 4.5$ $k=4.5$
$a = 10.5$ $a=10.5$
Look at the graph

enter image source here

Hence the general form of the equation is -

${(x - h)}^{2} = (4) (a) (x - k)$ $(x-h)^2 = (4)(a)(x-k)$

$x - 21)^{2} = (4) (10.5) (y - 4.5)$ $x-21)^2=(4)(10.5)(y-4.5)$

${(x - 21)}^{2} = 42 (y - 4.5)$ $(x-21)^2=42(y-4.5)$

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What is the equation in standard form of the parabola with a focus at (21,15) and a directrix of y= -6?

1 Answer

Explanation:

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