Find the Parabola with Focus (7,0) and Directrix x=-7 (7,0) x=-7

$(7, 0)$ $x = - 7$

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.

$(\frac{7 - 7}{2}, 0)$

Simplify the vertex.

Subtract $7$ from $7$ .

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

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 $p$ .

$p = 7 - 0$

Subtract $0$ from $7$ .

$p = 7$

Step 4

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

${(y - 0)}^{2} = 4 (7) (x - 0)$

Step 5

Simplify.

$y^{2} = 28 x$

Step 6

Find the Parabola with Focus (7,0) and Directrix x=-7 (7,0) x=-7

Related Questions

Support LCMGCF.com by disabling your adblocker.