Find the Parabola with Vertex (2,9) and Focus (2,6) (2,9) , (2,6)

$(2, 9)$ , $(2, 6)$

Step 1

Since the $x$ values are the same, 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 is $| p |$ . Subtract the $y$ coordinate of the vertex from the $y$ coordinate of the focus to find $p$ .

$6 - 9$

Subtract $9$ from $6$ .

$p = - 3$

Step 3

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

${(x - 2)}^{2} = 4 \cdot - 3 (y - 9)$

Step 4

Multiply $4$ by $- 3$ .

${(x - 2)}^{2} = - 12 (y - 9)$

Step 5