Find the vertex, focus, directrix, and focal width of the parabola. x = 3y^2

A parabola of the form, x = (a) y² + (b) y + c has a vertex, (h, k)

where

k = - b/2a

and

h = (a) k² + (b) k + c

In your case:

k = - 0/{2 (3) }

k = 0

h = 3 (0) ²

h = 0

The vertex is: (0, 0)

Let f = the focal width

f = 1/4a

f = 1/12

The focus is at

(h + f, k)

(1/12, 0)

The equation of the directrix is:

x = h - f

x = - 1/12