Find the Parabola with Focus (-5,-5) and Directrix y=7 (-5,-5) y=7

$(- 5, - 5)$ $y = 7$

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.

$(- 5, \frac{- 5 + 7}{2})$

Simplify the vertex.

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Add $- 5$ and $7$ .

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

Divide $2$ by $2$ .

$(- 5, 1)$

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 $p$ .

$p = - 5 - 1$

Subtract $1$ from $- 5$ .

$p = - 6$

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

${(x + 5)}^{2} = 4 (- 6) (y - 1)$

Simplify.

${(x + 5)}^{2} = - 24 (y - 1)$

Find the Parabola with Focus (-5,-5) and Directrix y=7 (-5,-5) y=7

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