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```									9.2 Parabola

Hyperbola/Parabola Quiz: FRIDAY
Concis Test: March 26
Parabola
   A parabola is defined in terms of a fixed
point, called the focus, and a fixed line,
called the directrix.

   In a parabola, the distance from any point,
P, on the parabola to the focus, F, is equal
to the shortest distance from P to the
directrix.
   That is, PF = PD for any point, P, on the
parabola.
Standard Equation of a
Parabola
   Horizontal directrix           Vertical directrix

1 2                             1 2
y    x                         x    y
4p                              4p
   p > 0: opens up                p > 0: opens right
   p < 0: opens down              p < 0: opens left
   You go up and down             You go left and right
the value of p to get           the value of p to get
directrix.
directrix
Something to keep in mind

   The focus should always be “in” your
curve.
   The directrix should always be
Example:
1 2
 Graph x  y . Label the vertex,
4
focus, and directrix.
You Try:
1 2
   Graph y x .  Label the vertex,
12
focus, and directrix.
Example:
   Write the standard equation of the
parabola with its vertex at the origin
and with the directrix y = 4.
   Sketch a graph if you need to.
You Try:

   Write the standard equation of the
parabola with its vertex at the origin
and with the directrix x = -6.

Next
Horizontal Directrix

Back

F(0,p)

y = -p
Vertical Directrix
x = -p
Back

F(p,0)
9.2 Continued

Hyperbola/Parabola Quiz: FRIDAY!
Conics Test: March 26
Standard Equation of a
Translated Parabola

Horizontal Directrix     Vertical Directrix
1                     1
yk     ( x  h) 2    xh     ( y  k) 2

4p                     4p
Example:
   Write the standard equation of the
parabola with its focus at (-3,2) and
with the directrix y = 4
   Sketch a graph if you need to.
You Try:

   Write the standard equation of the
parabola with its focus at (-6,4) and
with the directrix x = 2.
Example:

   Graph the parabola
y2 – 8y + 8x + 8 = 0. Label the vertex,
focus, and directrix.
Graph:
You Try:

   Graph the parabola
x2 – 6x + 6y + 18 = 0. Label the vertex,
focus, and directrix.
Graph:
Practice
   Parabola WS

THIS IS A LOT: PRACTICE!

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