Question

The focus of a parabola is located at (4,0), and the directrix is located at x =-4. Which equation represents the parabola?

Answer 1

Answer:

Step-by-step explanation:

One of the important things to remember about parabolas is that the vertex is directly in between the focus and the directrix. Our focus is at (4, 0) and the directrix is at (-4, 0), so that means that the vertex (h, k) is at the origin (0, 0). Another important thing to remember is that the distance between either the vertex and the focus or the vertex and the directrix is the p value, the value that tells us how stretched or compressed the parabola is. Another thing to remember is that a parabola will always wrap itself around the focus away from the directrix. So here's what we know then:

Our parabola opens to the right, the equation for that is

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

p = 4, and the vertex is (0, 0). Filling in the formula for the parabola using that info:

$(y-0)^2=4(4)(x-0)$ which simplifies a bit to

$y^2=16x$ and solving it for x:

$\frac{1}{16}y^2=x$