the equation of the parabola is (y-5)^2=5(x+8). Now I asked this earlier but that thread is farther down so no one sees it. He said the directrix is -9.25 but I think it is -1.25. Am I right?
no, the directrix is 1.25 from the vertex! (not from the origin)
therefore the directrix is at -8 -1.25
and the focus is at -8 + 1.25
It would be a good idea for you to draw this parabola. it looks like a round bottom cup on its side with the opening to the right. The middle of the bottom of the cup is at the vertex. The focus is to the right of the vertex. The directrix is a vertical line to the left of the focus.
By the way, all points on the parabola are equal distances from the directrix on the left of the vertex (measured horizontal, perpendicular to directrix line), and from the focus to the right of the vertex.
oh! Ok thank you. I already do have it graphed as that is required. Thank you for all the help.
To determine the directrix of the given parabola equation (y-5)^2 = 5(x+8), we can start by rewriting it in standard form, which is given by (y-k)^2 = 4a(x-h).
Comparing this to the given equation, we can identify the values of h, k, and a. From the given equation, we have h = -8, k = 5, and a = 5 / 4.
The standard form of the equation is (y-5)^2 = 4(5/4)(x+8).
Simplifying, we get (y-5)^2 = 5(x+8).
Now, to determine the directrix, we need to find the equation of the directrix in terms of y.
In a parabola, the directrix is a vertical line located at a distance of "a" units from the vertex, which is (h, k).
The vertex of the parabola is (-8, 5), and the value of "a" is 5/4.
Since the directrix is a vertical line, its equation will be in the form x = c, where c is a constant.
To find the value of c, we need to consider that the directrix is located on the side opposite to the parabola's focus, and it is equidistant from the focus and the vertex.
Here, the distance between the vertex (-8, 5) and the directrix is given by the absolute difference between the x-coordinates, which is |h - c|.
Using the distance formula, we get |(-8) - c| = 5/4.
Now we have two possibilities to consider:
1. (-8) - c = 5/4:
Solving for c, we have c = -8 - (5/4) = -32/4 - 5/4 = -37/4 = -9.25.
2. c - (-8) = 5/4:
Solving for c in this case, we have c + 8 = 5/4.
Moving 8 to the right side, we get c = 5/4 - 32/4 = -27/4 = -6.75.
After calculating the possible values of c, we find that c = -9.25 or c = -6.75.
Therefore, the directrix can be either x = -9.25 or x = -6.75.
Based on this analysis, it seems that you are correct in thinking that the directrix is -1.25 (-9.25 would be incorrect), as c = -6.75, not -9.25.