Question 1143057: Write the equation of the parabola in standard form and determine its vertex, focus, directrix, and axis.
2
y +4x -8y +28=0 Answer by greenestamps(13200) (Show Source):
I will guess that you want vertex form, since that is the form that tells you the most about the parabola.
The squared term is y, so the parabola opens right or left. The vertex form of the equation is
where the vertex is (h,k) and p is the directed distance from the directrix to the vertex and from the vertex to the focus.
Put the given equation in that form by completing the square and solving for x.
isolate the y terms complete the square in y isolate the x term solve for x
This is in vertex form, so the vertex is (-3,4).
The coefficient (-1/4) is 1/(4p), so p is -1. That means the focus is 1 unit to the left of the vertex and the directrix is 1 unit to the right of the vertex.
