Find the Directrix x=-2(y-1)^2

$x = - 2 {(y - 1)}^{2}$

Step 1

Use the vertex form, $x = a {(y - k)}^{2} + h$ , to determine the values of $a$ , $h$ , and $k$ .

$a = - 2$

$h = 0$

$k = 1$

Step 2

Find the vertex $(h, k)$ .

$(0, 1)$

Step 3

Find $p$ , the distance from the vertex to the focus.

Find the distance from the vertex to a focus of the parabola by using the following formula.

$\frac{1}{4 a}$

Substitute the value of $a$ into the formula.

$\frac{1}{4 \cdot - 2}$

Simplify.

Multiply $4$ by $- 2$ .

$\frac{1}{- 8}$

Move the negative in front of the fraction.

$- \frac{1}{8}$

Step 4

Find the directrix.

The directrix of a parabola is the vertical line found by subtracting $p$ from the x-coordinate $h$ of the vertex if the parabola opens left or right.

$x = h - p$

Substitute the known values of $p$ and $h$ into the formula and simplify.

$x = \frac{1}{8}$

Step 5

Find the Directrix x=-2(y-1)^2

Related Questions

Support LCMGCF.com by disabling your adblocker.