SOLUTION: What is the equation of the parabola with a focus at (0, -5) and directrix y = 5?

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Question 893188: What is the equation of the parabola with a focus at (0, -5) and directrix y = 5?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The parabola is the set of points (x,y) equally distant from (0,-5) as from (x,5).

DISTANCE FORMULA will let you derive the specific parabola.

sqrt%28%28x-0%29%5E2%2B%28y-%28-5%29%29%5E2%29=sqrt%28%28x-x%29%5E2%2B%28y-5%29%5E2%29
sqrt%28x%5E2%2B%28y%2B5%29%5E2%29=sqrt%280%2B%28y-5%29%5E2%29
x%5E2%2B%28y%2B5%29%5E2=%28y-5%29%5E2
Symmetric Property of Equality:
%28y-5%29%5E2=x%5E2%2B%28y%2B5%29%5E2
y%5E2-10y%2B25=x%5E2%2By%5E2%2B10y%2B25
-10y=x%5E2%2B10y
-20y=x%5E2
20y=-x%5E2
highlight%28y=-%281%2F20%29x%5E2%29