Final answer:
The correct answer for the equation of a parabola with a focus at (2,0) and directrix at x=-2 is y = (1/16)(x-2)^2 and the focal width is 16, as the focal length is 4.
Step-by-step explanation:
The given focus is at (2,0) and the directrix is the line x=-2. In order to find the correct equation for a parabola with a vertical axis of symmetry, it is important to note that the distance from the focus to the directrix (denoted as f) is equal to the distance from the vertex to the directrix. Since the directrix is at x=-2 and the focus is at (2,0), this distance is 2 - (-2) which equals 4. Therefore, the focal length f is 4. The focal width of the parabola, which is 4 times the focal length (4f), is 16, not 8. The standard form for a parabola with a focus of (h,k) and a directrix of x=k-p (where p is the distance from the vertex to the directrix) is (x-h)^2 = 4p(y-k). Applying this to the given focus and directrix, we get the equation (x-2)^2 = 16y, which can be simplified to y = (1/16)(x-2)^2. The correct answer is that the equation of the parabola is y = (1/16)(x-2)^2 and the focal width is 16.