Find the Parabola with Vertex (0,0) and Directrix y=4 (0,0) y=4

$(0, 0)$ $y = 4$

Step 1

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

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

Step 2

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 value of the directrix from the $y$ coordinate of the vertex to find $p$ .

$p = 0 - 4$

Subtract $4$ from $0$ .

$p = - 4$

Step 3

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

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

Step 4

Simplify.

$x^{2} = - 16 y$

Step 5

Find the Parabola with Vertex (0,0) and Directrix y=4 (0,0) y=4

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