Homework Help: Arriving at parabola formula via distance formula

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1. Dec 23, 2015

ducmod

1. The problem statement, all variables and given/known data
Hello!

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. Dec 23, 2015

Simon Bridge

Did you try subtracting (y-k)^2 from both sides, expanding the RHS, and grouping terms?

3. Dec 23, 2015

ducmod

I did, but didn't arrive at the correct outcome. Your question implies that I have to give it another try )

4. Dec 23, 2015

Simon Bridge

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) ...

5. Dec 23, 2015

Samy_A

The LHS is not what you want.