SOLUTION: From the equation, find the vertex, focus, directrix, and latus rectum. {{{(y-4)^2 = -8(x+3)}}} Please show me steps because i have been trying since yesterday and kept getti

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: From the equation, find the vertex, focus, directrix, and latus rectum. {{{(y-4)^2 = -8(x+3)}}} Please show me steps because i have been trying since yesterday and kept getti      Log On


   



Question 1036048: From the equation, find the vertex, focus, directrix, and latus rectum.
%28y-4%29%5E2+=+-8%28x%2B3%29
Please show me steps because i have been trying since yesterday and kept getting my answers wrong. Thankyou!

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
That is a form which you could get if you were given the focus and directrix and then derived the equation shown. The process would have gone like any of these:

Deriving parabola equation, vertex at Origin, horizontal symmetry axis
-
Deriving parabola equation, vertex not at Origin, vertical symmetry axis

You can read some information directly from the equation which you have.
The vertex is (-3,4).

The negative coefficient on the x side tells you that this has a graph with horizontal symmetry axis and the parabola opens toward the left, and vertex is a rightmost point on the parabola.

A value p is the distance between the vertex and either the focus or directrix. You have 8=4p, which is what you learn in making the derivation. You can solve for p and determine the focus and the directrix.