# How do you find the equation of a parabola with vertex at the origin and focus (2,0)?

Jun 26, 2018

See below for an explanation!

#### Explanation:

Since the focus is to the right of the parabola's vertex on a graph, and since the focus is always contained within the parabola, the parabola faces right. The formula for a right-facing parabola is

$x - h = \frac{1}{4 p} {\left(y - k\right)}^{2}$

Since the vertex is the origin, there aren't any $h$ or $k$ values:

$x = \frac{1}{4 p} {y}^{2}$

You may know that $p$ is the distance from the vertex of a parabola to both its focus and directrix. The focus is 2 units away, so $p = 2$. Because of this, the scale factor would be $\frac{1}{4 \cdot 2} = \frac{1}{8}$. Our final equation is

$x = \frac{1}{8} {y}^{2}$

Hope this helped. Have a nice day!