Find the Parabola with Vertex (2,2) and Directrix y=2.5 (2,2) y=2.5

$(2, 2)$ $y = 2.5$

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 $p$ .

$p = 2 - 2.5$

Subtract $2.5$ from $2$ .

$p = - 0.5$

Step 3

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

${(x - 2)}^{2} = 4 (- 0.5) (y - 2)$

Step 4

Simplify.

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

Step 5

Find the Parabola with Vertex (2,2) and Directrix y=2.5 (2,2) y=2.5

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