The focus and directrix are a point and line that define a parabola. The focus, which lies inside the parabola, is always the same distance from a specific point on the surface of the parabola as that point is from the directrix. The directrix is outside of the parabola and forms a 90degree angle with its axis of symmetry. Finding the focus and directrix in a parabola is a moderately easy task that can be completed using the equation of a given parabola.

Rearrange the equation of the parabola. The vertex form of the parabola equation is y = a(x  h)^2 + k. As an example, consider the parabola y = 2(x  4)^2 + 6 as an example. The form you need the equation to be in is (x  h)^2 = 4p(y  k). You can rearrange the equation by subtracting "k" from "y" and dividing both sides of the equation by "a." The example is rearranged as (x  4)^2 =1/2(y  6). After doing this, you should note that 4p = 1/a. In the example, 4p=1/2

Calculate the yvalue for the parabola's focus. The xvalue is already known to be "h" in the parabola's equation. The yvalue now needs to be found. It can be found by solving for "p" in the equation 4p = 1/a. After dividing both sides by four, you will find that p = 1/4a or 1/8 in the example. The yvalue for the parabola's focus is k + p. The focus of the parabola is therefore the point located at (h, k + p) or (4, 49/8).

Find the parabola's directrix. The directrix is opposite the focus. It, therefore, has the equation y = k  p or, in the example, y = 47/8.