Standard Equation: x<sup>2</sup>= 4py y<sup>2</sup>= 4px
vertical parabola horizontal parabola
axis y-axis x-axis
vertex (0,0) (0,0)
p is the focus of p>0 opens up p>0 opens right
p<0 opens down p<0 opens left
focus (0,p) (p,0)
directrix y = -p x = -p
length of latus rectum 4|p| 4|p|
Graph x2= 6y
The standard equation is x2 = 4py,
which implies a vertical parabola with the vertex at the origin and the axis is the y-axis.
4p = 6
P > 0, the parabola opens up and the focus is at (0, 3/2)
The directrix is the line y = -3/2
4|p| = 6, the end points of the latus rectum is (3, 3/2) and (-3, 3/2)
Graph y2= -16y
The equation is in the form: y2 = 4px,
which implies a horizontal parabola with the vertex at the origin and the axis is the x-axis.
4p = -16
p = -4
p < 0, the parabola opens left and the focus is at ( -4,0).
The directrix is the line x = 4.
Â± 2p = Â± 8; \ the end points of the latus rectum are points (-4, 8) and (-4, -8).