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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
        your focus and                  your focus and
                                        directrix.
        directrix
Something to keep in mind

   The focus should always be “in” your
    curve.
   The directrix should always be
    “outside” of your curve.
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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