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

1 Answer
Oct 22, 2017

Vertex: (0,0)

Focus: (5/2,0)

Directrix: x=-5/2

Explanation:

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

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

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

10x=4ax

10=4a

5=2a

therefore a=5/2

So, the coordinates of the focus are (5/2,0).

The equation of the directrix of a concave right parabola is x=-a.
This means the directrix for this parabola is x=-5/2