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Homework Help: Find the extremities of latus rectum of the parabola

  1. Sep 2, 2010 #1
    Find the extremities of latus rectum of the parabola y=(x^2)-2x+3.

    Please someone post its solution. Ans. is (1/2,9/4) (3/2,9/4).

    i just need full solution. I tried a lot but didn't get this correct answer.
     
  2. jcsd
  3. Sep 2, 2010 #2

    Mentallic

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    Re: Parabola

    Show us what you've tried in order to find the equation of the latus rectum.
     
  4. Sep 2, 2010 #3
    Re: Parabola

    y=x^2-2x+3
    x^2-2x=y-3
    x^2-2x+1=y-3+1
    (x-1)^2=1(y-2)

    let X=x-1 and Y=y-2
    then equation becomes X^2=Y

    on comparing it with x^2=4ay which is general form of parabolic equations we get
    a=1/4

    so according to me extremities of latus rectum should be (0,1/4) (0,-1/4)....


    I'm in 11th grade and i just started this topic first time few days back. So i'm very new for it..
     
  5. Sep 2, 2010 #4
    Re: Parabola

    y=x^2-2x+3
    x^2-2x=y-3
    x^2-2x+1=y-3+1
    (x-1)^2=1(y-2)

    let X=x-1 and Y=y-2
    then equation becomes X^2=Y

    on comparing it with x^2=4ay which is general form of parabolic equations we get
    a=1/4

    so according to me extremities of latus rectum should be (0,1/4) (0,-1/4)....


    I'm in 11th grade and i just started this topic first time few days back. So i'm very new for it..
     
  6. Sep 2, 2010 #5

    Mentallic

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    Re: Parabola

    They should be those coordinates for a parabola that is y=x2 but yours isn't that, it is y-2=(x-1)2. for a parabola y=x2 the vertex is at (0,0) and focus is at (0,a) which suggests that for a parabola is the form y-k=(x-h)2 the vertex is at (h,k) and the focus is then at...?
     
  7. Sep 2, 2010 #6
    Re: Parabola

    Hmmm. I dont know. Please you tell me
     
  8. Sep 2, 2010 #7

    Mentallic

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    Re: Parabola

    If the vertex is at (0,0) and the focus is at (0,a) then the focus is always a units above the vertex (actually, inside the parabola would be better since if the parabola is curving downwards then the focus is a units down). Then for a parabola with centre (h,k) the focus will be?
     
  9. Sep 2, 2010 #8
    Re: Parabola

    Focus should be (h, k+a). And what about latus rectum
     
  10. Sep 2, 2010 #9
    Re: Parabola

    Hey i got the correct ans. Thanks, thanks a lot for helping me
     
  11. Sep 2, 2010 #10

    Mentallic

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    Re: Parabola

    That's it! :smile: The latus rectum is just y=k+a, so you find where that line intercepts the parabola.

    No problem, take care.
     
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