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Can someone tell me if I am right?

I need to find the equation of a parabola. I am not sure if this is the correct way or if I have the correct answer.

Vertex at origin, focus is at (0,3)

Equation of parabola
vertex (0,0) focus (0,3)
focus (h,k+p)
directrix y=-3
a=(-1/12) h=0 k=0
my answer is: y=(-1/12)(x^2)+0

  • Algebra -

    shouldn't your parabola open upwards ?
    your -1/12x^2.... makes it open down.

    I do it this way:
    let P(x,y) be any point on the parabola
    by definition, the distance from P to the focal point is equal to the distance to the directrix --->
    √(x^2 + (y-3)^2) = √(y+3)^2)

    square both sides, and simplify to get

    y = (1/12)x^2

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