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

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Answer 1 · 2017-10-22T01:39:53

Vertex: #(0,0)#

Focus: #(5/2,0)#

Directrix: #x=-5/2#

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#