SOLUTION: Prove that any given point on a parabola is the same distance from the focus and directrix. Fast help wold be great, I've been trying to figure this out for a week already. Tha

Algebra ->  Coordinate-system -> SOLUTION: Prove that any given point on a parabola is the same distance from the focus and directrix. Fast help wold be great, I've been trying to figure this out for a week already. Tha      Log On


   



Question 1026295: Prove that any given point on a parabola is the same distance from the focus and directrix.
Fast help wold be great, I've been trying to figure this out for a week already.
Thanks in advance!

Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Prove that any given point on a parabola is the same distance from the focus and directrix.
------------
That's the definition of a parabola:
The locus of points equidistant from a point and a line.
----
It makes no sense to say "This is what it is." and then say "prove it."

Answer by ikleyn(52771) About Me  (Show Source):
You can put this solution on YOUR website!
.
Prove that any given point on a parabola is the same distance from the focus and directrix.
Fast help wold be great, I've been trying to figure this out for a week already.
Thanks in advance!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For the proof, see the lesson Parabola focal property in this site.