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

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

Step 1

Since the directrix is horizontal, use the equation of a parabola that opens left or right.

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

Step 2

Find the vertex.

The vertex $(h, k)$ is halfway between the directrix and focus. Find the $x$ coordinate of the vertex using the formula $x = \frac{x coordinate of focus + directrix}{2}$ . The $y$ coordinate will be the same as the $y$ coordinate of the focus.

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

Simplify the vertex.

Add $- 3$ and $3$ .

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

Divide $0$ by $2$ .

$(0, 0)$

Step 3

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 $x$ coordinate of the vertex from the $x$ coordinate of the focus to find $p$ .

$p = - 3 - 0$

Subtract $0$ from $- 3$ .

$p = - 3$

Step 4

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

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

Step 5

Simplify.

$y^{2} = - 12 x$

Step 6

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

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