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Homework Help: Arriving at parabola formula via distance formula

  1. Dec 23, 2015 #1
    1. The problem statement, all variables and given/known data

    Please, help me to get through equations. I can't derive the equation in the way suggested.

    Here is the definition:
    So, if vertex is at (h, k) and there is a given point on a parabola at (x; y), then focus is at (h; k + p),
    and point of a directrix is at (x; k - p).

    Thus the distance formula should be (I am dropping the square root):
    (x - h)^2 + (y - k)^2 = (y - k + p)^2

    How did they come to (x - h)^2 = 4p(y - k) ?

    Thank you!
    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Dec 23, 2015 #2

    Simon Bridge

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    Did you try subtracting (y-k)^2 from both sides, expanding the RHS, and grouping terms?
  4. Dec 23, 2015 #3
    I did, but didn't arrive at the correct outcome. Your question implies that I have to give it another try )
  5. Dec 23, 2015 #4

    Simon Bridge

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    Well it just means that I don't know what you've tried ... go over it more carefully - double check your starting point.
    If P is a point on the parabola and D is the corresponding point on the directrix, then a parabola with focal point F has: |PF| = |PD|
    From what you've written; P=(x,y), D=(x,k-p), F=(h,k+p) ...
  6. Dec 23, 2015 #5


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    The LHS is not what you want.
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