Question 679421: How do i write equations for parabolas with a fraction directrix? For example, vertex (-6,-9) directrix -47/8. I think I use the equation y=a(x-h)^2+k?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! How do i write equations for parabolas with a fraction directrix? For example, vertex (-6,-9) directrix -47/8. I think I use the equation y=a(x-h)^2+k?
**
Equations to use for this type of problem:
There are 4 configurations as follows:
(1) (x-h)^2=4p(y-k), (h,k)=(x,y) coordinates of the vertex, parabola opens upward.
(2) (x-h)^2=-4p(y-k), (h,k)=(x,y) coordinates of the vertex, parabola opens downward.
(3) (y-k)^2=4p(x-h), (h,k)=(x,y) coordinates of the vertex, parabola opens rightward.
(4) (y-k)^2=-4p(x-h), (h,k)=(x,y) coordinates of the vertex, parabola opens leftward.
In each of these 4 configurations, p=distance from directrix and focus to vertex on the axis of symmetry
The directrix is always on the convex side of the parabola and the focal point equally distant from the vertex on the other (concave) side. The directrix is a line and must be written as a formula,ie, x=-47/8, or y=-47/8, for your problem. This will determine which of the configurations above you are working with.
|
|
|
