Find the Focus x=1/24(y-4)^2

$x = \frac{1}{24} {(y - 4)}^{2}$

Step 1

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

$a = \frac{1}{24}$

$h = 0$

$k = 4$

Step 2

Find the vertex $(h, k)$ .

$(0, 4)$

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.

$\frac{1}{4 \cdot \frac{1}{24}}$

Simplify.

Combine $4$ and $\frac{1}{24}$ .

$\frac{1}{\frac{4}{24}}$

Cancel the common factor of $4$ and $24$ .

Factor $4$ out of $4$ .

$\frac{1}{\frac{4 (1)}{24}}$

Cancel the common factors.

Factor $4$ out of $24$ .

$\frac{1}{\frac{4 \cdot 1}{4 \cdot 6}}$

Cancel the common factor.

$\frac{1}{\frac{4 \cdot 1}{4 \cdot 6}}$

Rewrite the expression.

$\frac{1}{\frac{1}{6}}$

Multiply the numerator by the reciprocal of the denominator.

$1 \cdot 6$

Multiply $6$ by $1$ .

$6$

Step 4

Find the focus.

The focus of a parabola can be found by adding $p$ to the x-coordinate $h$ if the parabola opens left or right.

$(h + p, k)$

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

$(6, 4)$

Step 5