I need like step through step ways to write an equation for a parabola.

So like here are two examples we can use:

Focus(1,4) Diretrix:y=2


Focus(-2,-6) Latus Rectum=8

I need like step through step ways to write an equation for a parabola.

So like here are two examples we can use:

Focus(1,4) Directrix: y=2

Focus(-2,-6) Latus Rectum=8

There's a lot of information about parabolas here:

Parabola - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Parabola)

The basic equations for parabolas are

(x-h)^2=4p(y-k) (parabola's axis parallel to y-axis)

or

(y-k)^2=4p(x-h) (parabola's axis parallel to x-axis)

The vertex is (x,k); the focus is (h, k+p); the directrix is y=k-p where p is the distance from the vertex to the focus.

In your first case, you have Focus(1,4) Directrix: y=2

h = 1
k+p=4
k-p=2
so k=3 and p=1

From the directrix, y=2, the parabola's axis is parallel to the y-axis.

(x-h)^2=4p(y-k) (parabola's axis parallel to y-axis)

(x-1)^2=4(y-3)

You can multiply it out

x^2-2x+1=4y-12

You should work on the second problem. The Wikipedia article has information on it.

I don't understand how to do this question:A parabola has vertex 0,0 and focus on coordinate axis. Write equation of parabola if; a) the focus is; 1) 4, 0 2)-6, 0 3)0, 3. The directrix is the line defined by y=8

Kumar, you can start your own thread in order to have help with your question.