Find the Directrix x=-1/4(y-4)^2-2

$x = \frac{- 1}{4} {(y - 4)}^{2} - 2$

Step 1

Isolate $x$ to the left side of the equation.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{1}{4} {(y - 4)}^{2} - 2$

Combine ${(y - 4)}^{2}$ and $\frac{1}{4}$ .

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

Reorder terms.

$x = - \frac{1}{4} \cdot {(y - 4)}^{2} - 2$

Step 2

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

$a = - \frac{1}{4}$

$h = - 2$

$k = 4$

Step 3

Find the vertex $(h, k)$ .

$(- 2, 4)$

Step 4

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.

$\frac{1}{4 \cdot (- \frac{1}{4})}$

Simplify.

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- 1 (- 1)}{4 \cdot (- \frac{1}{4})}$

Move the negative in front of the fraction.

$- \frac{1}{4 (\frac{1}{4})}$

Combine $4$ and $\frac{1}{4}$ .

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

Divide $4$ by $4$ .

$- \frac{1}{1}$

Cancel the common factor of $1$ .

Cancel the common factor.

$- \frac{1}{1}$

Rewrite the expression.

$- 1 \cdot 1$

Multiply $- 1$ by $1$ .

$- 1$

Step 5

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.

$x = - 1$

Step 6

Find the Directrix x=-1/4(y-4)^2-2

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