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-   -   Finding the vertex, focus and the coordinates of the end of the latus rectum (https://www.askmehelpdesk.com/showthread.php?t=369832)

  • Jun 28, 2009, 06:16 AM
    akotoh
    finding the vertex, focus and the coordinates of the end of the latus rectum
    hello... :) I hope u can help me with this.. I find it very difficult for me bcoz our prof gives us example but this problems are not d sme in any of his example. :( I've tried my best to answer this problem but still n0thing happens.. I hope u can really help me..

    1.) x^2-2x-y=0
    I thot diz will become:
    x^2=2x+y

    2.) y^2+3x-2y+7=0
    y^2=-3x+2y-7

    3.) 2y^2-5x+3y-7=0
    2y^2=5x-3y+7
  • Jun 28, 2009, 07:38 AM
    galactus
    With this? Becoz? What language is that?
  • Jun 28, 2009, 08:53 AM
    Unknown008

    Ah, the youngsters of these days...

    I think that you need to put in the form of



    Am I right? I just have found some questions about those, but haven't done it at school yet.
  • Jun 28, 2009, 04:57 PM
    akotoh
    Mr. Galactum.. please help me in this problem.. :(
  • Jun 28, 2009, 05:09 PM
    akotoh

    Sorry for the spelling mr. galactum.. that should be: "with this" and "because".
  • Jun 29, 2009, 08:24 AM
    Unknown008

    *Sigh* it's galactus, akotoh, not galactum
  • Jun 29, 2009, 03:45 PM
    galactus
    The vertex is halfway between the focus and the directrix. The distance from the focus to

    the vertex or from the vertex to the directrix is normally indicated by 'p'.

    If the parabola has an axis of symmetry parallel to the x-axis, then it has equation

    . Where (h,k) are the coordinates of the vertex.

    If it opens in the positive x direction, then it has a + sign. If it opens in the negative x direction, then it has a - sign.

    If the parabola has an axis of symmetry parallel to the y-axis, then it has equation

    .

    If it opens up then it has a + sign and if it opens down, then it has a negative sign.

    See if you can get them in the above forms.


    Quote:

    1.)
    You could rewrite this one as

    It has focus at (1, -3/4)
    Vertex at (1,-1)
    Directrix at y=-5/4

    The vertex can be found by In this case, a=1 and b=-2

    . Sub back into the equation and get y=-1

    Quote:

    2.)
    You could write this one as

    This one opens to the left. It has vertex at (-2,1), Focus at (11/4,1) and directrix at x=-5/4

    Quote:

    3.)
    Opens to the right.



    Vertex at (-13/8, -3/4), Focus at (-1,-3/4), Directrix at x = -9/4

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