Finding parabola parameter given 2 points How can I determine which is the directrix and the focus of a parabola and what is the distance between those points, only knowing that this parabola has its symmetry axis = OX and its passes through the points P1 and P2?
EDIT: 
Guys, if possible, someone post an example using real numbers please, I think it will be more clear to me (both answers are great, but I'm still having problems to understand, sorry). I'm working with points P1(0,0) P2(6,6) and I need to found p (distance between directrix and focus). Can you guys explain using these numbers?
 A: Let's use the following form for the parabola:
$$y=a(x-h)^2+k$$
Distance from vertex $(h,k)$ to your directrix and focus is calculated using the following formula where $p$ is the distance.
$$a=\frac{1}{4p}$$
If $a$ is positive, the equation for your directrix will be as follows:
$$y=k-p$$
Also, the coordinates of the focus will be the following with $+a$:
$$(h,k+p)$$
If $a$ is negative, there are simply a few sign changes. Directrix equation with $-a$:
$$y=k+p$$
Focus with $-a$:
$$(h, k-p)$$
Hopefully this helped.
A: The standard equation of the parabola with its axis (symmetric axis=OX) coincident with the x-axis   & vertex at the point $(k, 0)$ on the x-axis is $$\color{blue}{y^2=4a(x-x_1)}$$ 
Where, $a$ & $k$ are arbitrary constants.
Now, satisfying the above equation of parabola by the coordinates of two given point $P_1(x_1, y_1)$ & $P_2(x_2, y_2)$. We get two linear equations in terms of $a$ & $k$ which are determined by solving them. Then we have 
The equation of the directrix: $$x-k=-a\iff \color{red}{x=k-a}$$
The focus of the parabola: $$(x-k=a, y=0)\equiv\color{red}{(k+a, 0)}$$ 
