Find the Parabola with Focus (0,-3) and Directrix y=3 (0,-3) y=3

$(0, - 3)$ $y = 3$

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.

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.

$(0, \frac{- 3 + 3}{2})$

Simplify the vertex.

Add $- 3$ and $3$ .

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

Divide $0$ by $2$ .

$(0, 0)$

Find the distance from the focus to the vertex.

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 $p$ .

$p = - 3 - 0$

Subtract $0$ from $- 3$ .

$p = - 3$

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

${(x - 0)}^{2} = 4 (- 3) (y - 0)$

Simplify.

$x^{2} = - 12 y$

Find the Parabola with Focus (0,-3) and Directrix y=3 (0,-3) y=3

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