Find the Parabola with Focus (0,5) and Directrix y=-5 (0,5) , y=-5

$(0, 5)$ , $y = - 5$

Since the directrix is vertical, use the equation of a parabola that opens up or down.

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

Find the vertex.

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The vertex $(h, k)$ is halfway between the directrix and focus. Find the $y$ coordinate of the vertex using the formula $y = \frac{y coordinate of focus + directrix}{2}$ . The $x$ coordinate will be the same as the $x$ coordinate of the focus.

$(0, \frac{5 - 5}{2})$

Simplify the vertex.

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Subtract $5$ from $5$ .

$(0, \frac{0}{2})$

Divide $0$ by $2$ .

$(0, 0)$

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 $| p |$ . Subtract the $y$ coordinate of the vertex from the $y$ coordinate of the focus to find $p$ .

$p = 5 - 0$

Subtract $0$ from $5$ .

$p = 5$

Substitute in the known values for the variables into the equation ${(x - h)}^{2} = 4 p (y - k)$ .

${(x - 0)}^{2} = 4 (5) (y - 0)$

Simplify.

$x^{2} = 20 y$

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