Question

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

Answer 1

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