SOLUTION: If given the equation of a parabola, how do i find the focus?

Question 450434: If given the equation of a parabola, how do i find the focus?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
If given the equation of a parabola, how do i find the focus?
..
There are 4 basic equations for the parabola from which you can find the focus as follows:
1) x^2=4py (parabola opens upwards, axis of symmetry vertical)
2) x^2=-4py (parabola opens downwards, axis of symmetry vertical)
3) y^2=4px (parabola opens rightwards, axis of symmetry horizontal)
4) y^2=-4px (parabola opens leftwards, axis of symmetry horizontal)
..
In all four cases, if you find p, you can find the focus. 4p is the coefficient of x or y as the case might be. p is also the distance from vertex to focus and from vertex to directrix on the axis of symmetry. If you know 2 out of the 3 items( p, vertex, and directrix) you should be able to find the focus.
RELATED QUESTIONS
How do I find equation of a parabola given just the focus and... (answered by josgarithmetic)

how do I find the focus of a parabola? please explain in the simplest way... (answered by lwsshak3)

how do you write the equation of a parabola given the vertex at origin and focus of... (answered by lwsshak3)

if you are given a parabola and the focal diameter is 12, how do you find what the focus... (answered by lwsshak3)

How do I find an equation of the parabola with focus(0,-pi) and directrix y =... (answered by lwsshak3)

How do you find the equation of a parabola with a vertex at (0,0) and a focus at... (answered by josgarithmetic)

Find an equation of a parabola satisfying the given conditions. Focus(0-pie),directrix (answered by stanbon)

find the equation of a parabola given focus (-2,3) directrix... (answered by lwsshak3)

Write an equation of a parabola with the given vertex and focus. Vertex (-3,2) focus... (answered by josgarithmetic)