Locus and Parabola (1 Viewer)

[User5555555]

Does anyone have a formula sheet for this topic? Also How would you go about setting the working out for these types of questions?

I did not pay attention in class and need to know this.

That is, what the directrix is, the focus, how do you find it, how do you convert a word question or equation into a graph or something. Please Help

 

[Shazer2]

I find that with these questions your best bet is to graph them. So the general form for a parabola is:



From that you can determine the vertex, in this case (0, 0) but for a parabola with vertex (-1, 4) the equation would read:



The represents the focal length, so to find the focus you simply add a (the focal length) to your vertex. If in this case was 3, then your focus is at (-1, 7). The directrix is the line that is the same distance from the vertex as the focus. Therefore, the vertex is the midpoint between the focus and the directrix. From the origin, the directrix is at y=-a.

Then you have alternate forms for your general parabola. represents a concave down parabola, represents a horizontal parabola.