SOLUTION: How do you find the equation of a parabola with a vertex at (0,0) and a focus at (0,2)?

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Question 966781: How do you find the equation of a parabola with a vertex at (0,0) and a focus at (0,2)?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
So many questions of this kind are asked. Use the definition of a parabola and the distance formula. Simplify the equation resulting.

Directrix is (x,-2)

sqrt%28%28x-0%29%5E2%2B%28y-2%29%5E2%29=sqrt%28%28x-x%29%5E2%2B%28y-%28-2%29%29%5E2%29



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Simplification steps:

sqrt%28x%5E2%2B%28y-2%29%5E2%29=sqrt%280%2B%28y%2B2%29%5E2%29
sqrt%28x%5E2%2B%28y-2%29%5E2%29=sqrt%28%28y%2B2%29%5E2%29
Square both sides:
x%5E2%2B%28y-2%29%5E2=%28y%2B2%29%5E2
x%5E2%2By%5E2-4y%2B4=y%5E2%2B4y%2B4
x%5E2-4y%2B4=4y%2B4
x%5E2=4y%2B4%2B4y-4
highlight%28x%5E2=8y%29
OR
highlight%28y=%281%2F8%29x%5E2%29