# How do you find the vertex, focus, and directrix of the parabola 10x=y^2?

Oct 22, 2017

Vertex: $\left(0 , 0\right)$

Focus: $\left(\frac{5}{2} , 0\right)$

Directrix: $x = - \frac{5}{2}$

#### Explanation:

This is a concave right parabola. You can tell because the formula given is in the form ${y}^{2} = 4 a x$.

The vertex is $\left(0 , 0\right)$, at the origin. We know this because no transformations have been applied to the parabola.

The focus of a concave right parabola as $\left(a , 0\right)$. We can find $a$ by solving:

$10 x = 4 a x$

$10 = 4 a$

$5 = 2 a$

$\therefore a = \frac{5}{2}$

So, the coordinates of the focus are $\left(\frac{5}{2} , 0\right)$.

The equation of the directrix of a concave right parabola is $x = - a$.
This means the directrix for this parabola is $x = - \frac{5}{2}$