What is the equation of the parabola with a vertex (0,0) and the focus (0,-5).

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The equation of a vertical parabola is given by;

`4p(y-k) = (x-h)^2`

Where;

p = distance to vertex from focus point

(h,k) = coordinates of vertex

(h,p+k) = cordinates of focus point

It is given that vertex `(0,0)` and the focus `(0,-5)` .

`h = 0`

`k = 0`

`p+k = -5 rarr p+0 = -5 rarr p = -5`

`4p(y-k) = (x-h)^2`

`4xx(-5)(y-0) = (x-0)^2`

`y = x^2/20`

So the equation of the parabola is `y = x^2/20`

Sources:

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