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Math Help - parabola equations

  1. #1
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    parabola equations

    I am want to derive some of the equations for parabolas with vertex at (h,k). I wrote the equation below directly from the definition. I'm having a hard time obtaining any of the standard forms for parabolas from this definition. For example: y = a(x-h)^2 +K is one such equation I would like to derive. I need to know if I'm setting this up right.

    p=\sqrt{(x-h)^2+[y-(k+p)]^2}

    p^2=(x-h)^2+y^2-2y(k+p) + (k+p)^2

    (x-h)^2=-y^2+2yk-k^2+2p(y-k)

    (x-h)^2=-(y-k)^2+2p(y-k)

    As you can see I'm having trouble converting this into either form:

    (x-h)^2=4p(y-k)

    y=a(x-h)^2+k

    Where a =1/4p
    Attached Thumbnails Attached Thumbnails parabola equations-equation.bmp   parabola equations-parabola.jpg  
    Last edited by adkinsjr; July 5th 2009 at 08:10 AM.
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by adkinsjr View Post
    I am want to derive some of the equations for parabolas with vertex at (h,k). I wrote the equation below directly from the definition. I'm having a hard time obtaining any of the standard forms for parabolas from this definition. For example: y = a(x-h)^2 +K is one such equation I would like to derive. I need to know if I'm setting this up right.
    What is P here?

    distance of (x,y) from (h,k+p)
    = \sqrt{(x-h)^2+(y-k-p)^2}

    distance of (x,y) from line y=k-p
    = y-k+p

    Can you proceed now?
    Last edited by malaygoel; July 4th 2009 at 10:22 PM.
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  3. #3
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    Quote Originally Posted by malaygoel View Post
    What is P here?

    distance of (x,y) from (h,k+p)
    = \sqrt{(x-h)^2+(y-k-p)^2}

    distance of (x,y) from line y=k-p
    = y-k+p

    Can you proceed now?
    P is the distance from (x,y) to the line y = k - P



    I should be able to proceed from here. I just needed to know if I was setting this up right. I didn't want to waste time with the algebra if I didn't have the rigth equation.
    Last edited by adkinsjr; July 5th 2009 at 06:09 AM.
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  4. #4
    Super Member malaygoel's Avatar
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    Quote Originally Posted by adkinsjr View Post
    P is the distance from (x,y) to the line y = k - P

    P = y - k + p

    I should be able to proceed from here. I just needed to know if I was setting this up right. I didn't want to waste time with the algebra if I didn't have the rigth equation.
    yeah, you are setting up the right equation.
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