Finding an equation of a parabola

Find the equation of a parabola with its vertex at the origin if its directrix is x=6
A. x=(1/24)y^2
B. x=-24y^2
C. x= (-1/24)y^2
D. x=6y^2

I don't know how to get the answer... Can someone explain this ?

The directrix is vertical, which means that your parabola is horizontal.

standard form of a horizontal parabola (conic section) can be written as

(x - h) = 4p(y - k)^2

where your center is at (h,k) and p is the distance from the vertex to the focus and directrix. Now your center is at the origin, which means that (h,k) is (0, 0)

(x - 0) = 4p(y - 0)^2
x = 4py^2

Now you know that the center is at the origin, which means that the directrix x=6 would be to the right. Then your parabola must open up on the left because a parabola will never cross its on directrix. If it opens to the left, the value of p will be -6, instead of 6.

x = 4(-6) y^2
x = -24 y^2

hope this helped!

here's some more information on conic sections: http://www.sparknotes.com/math/precalc/c…

Vertex (0, 0):

h = 0
k = 0

Directrix:

x = 6

Since the directrix is perpendicular to the x-axis, the parabola will be horizontally oriented and, since the directrix is to the right of the vertex, it will open to the left, so

p = h - x
p = 0 - 6
p = - 6

a = 1 / 4p
a = 1 / 4(- 6)
a = 1 / ( - 24)
a = - 1/24

Equation:

x = - 1/24 y²
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