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Find the vertex, focus, and the directrix of the parabola

  1. Mar 5, 2006 #1
    Find the vertex, focus, and the directrix of the parabola.

    I get tripped up sometimes, but I know how to find all of the stuff with an equation like this :
    (x+1)^2 +8(y+3) = 0

    But how do I find it with equations like this
    y^2=-6x

    or

    x+y^2=0

    Can you complete the square with only two terms?
     
  2. jcsd
  3. Mar 5, 2006 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Reverse x and y! That is, change x+ y2= 0 to x2+ y= 0 which you know how to do. Once you have found the vertex, focus, directrix for that, switch back: If you found (a,b) as the vertex of x2+y= 0, then (b,a) is the vertex of x+ y2= 0. If you found y= c as the directrix of x2+ y= 0, then the directrix of
    y2+ x= 0 is x= c.
     
  4. Mar 5, 2006 #3
    My work

    (x-h)^2=4p(y-k)
    since h and k are 0 then the vertex = (0,0)
    How do I find the focus and the directrix though?
    Focus maybe = 4p = -6 P= -3/2 so the focus (0,-3/2) ?????
    Directrix ?!?!?!?!?
     
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