10.2
Parabolas
JMerrill, 2010
Review—What are Conics
Conics are formed by the intersection of a plane and a
double-napped cone. There are 4 basic conic sections.
Notice that the plane does not pass through the
vertex. If that happens, the resulting figure is a
degenerate conic…
Degenerate Conics
Definition of the Parabola

A parabola is the set of all points (x, y) in
a plane that are equidistant from a fixed
line (directrix) and a fixed point (focus)
not on the line.
Equations
See p. 736
Orientation
State the direction in which each parabola
opens (the orientation).
 a) ( y  4)  12  x  2
left
 b) ( x  1)  8 y
down
up
 c) ( x  2)  2  y  3
right
 d) ( y  5)  x
2
2
2
2
Example: Find the coordinates of the vertex and focus, the
equation of the directrix, and graph the parabola
( x  2)  2  y  3
2
orientation:
 up
 vertex:
 (2, -3)
 Focus—find p
 (2, -2.5)


directrix:

y = -3.5
You will need to graph it in order to find
how wide the parabola opens
You Try
( y  5) 2  x
orientation:
 right
 vertex:
 (0, 5)
 focus:
 (.25, 5)
 directrix:


x = -.25
Finding the Equation
Find the standard form of the equation of
the parabola with vertex (2, 1) and focus
(2, 4)
 Draw what you know
 Is the axis of symmetry vertical or
horizontal?
 So the model is (x - h)2 = 4p(y – k)
 What is p? 3
 Equation?
(x - 2)2 = 12(y – 1)
