y = 4x^2 + 8x + 5
find the focal length, the focus and the directrix.
any help? much appreciated
Hey jv,
There is more than one way to approach this, so here is one way. Remember that a parabola is a curve consisting of all points in the coordinate plane that are the same distance from a given point (the focus) and a given line (the directrex). The focal length is the distance from the vertex to the focus.
Examples with solutions can be found here, as well as a number of other places on the net.
First, put the equation in this form:
You'll have to know how to complete the square. Do you?
I'll get you started:
Once you have it in the above form, apply the following information to find what you need:
Vertex
Focus
Directrex