1. 11.3 PARABOLAS Directrix (L): A line in a plane.
Focus (P): A point NOT on the directrix.
X is any point on the parabola

2. Axis: The line through the focus P ⊥ to the directrix L.
Vertex: The intersection of the axis with the parabola (midpoint of P to L).
Equation: For a nonzero real # P, parabolas have the following equations & characteristics:

3. x2 = 4py
y2 = 4px
Focus at (0, P)
Focus at (P, 0)
Directrix: y = -p
Directrix: x = -p
Axis of symmetry: y-axis
when vertex is on y-axis
Equation x = 0
Axis of symmetry: x-axis
when vertex is on x-axis Equation y = 0
If p > 0, then the parabola opens up.
If p > 0, then the parabola opens right.
If p < 0, then the parabola opens down.
If p < 0, then the parabola opens left.

4. Ex. #1 Find the equation of the parabola with vertex (0, 0) that satisfies the given information:  
a. axis y = 0
b. focus (3.5, 0)
passing through (2, 12)

5. Ex. #2 Find the focus & directrix.
x = ½ y2
b. x = -6y2

6. Ex. #3 Find the equation of the parabola centered at the origin & passing through the given points.
(3, ) & (3, )
b. (-2, -5) & (2, -5)