Find the Parabola with Focus (1,4) and Directrix x=5 (1,4) x=5

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

Simplify the vertex.

The distance from the focus to the vertex and from the vertex to the directrix is ${\displaystyle \left|p\right|}$. Subtract the ${\displaystyle x}$ coordinate of the vertex from the ${\displaystyle x}$ coordinate of the focus to find ${\displaystyle p}$.

Subtract ${\displaystyle 3}$ from ${\displaystyle 1}$.