Find the standard form of the equation of the parabola with a focus at (0, -10) and a directrix at y = 10
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keeping in mind that the distance from the vertex to the focus, is the exact same one as the distance from the vertex to the directrix, in the opposite direction
where do you think is the vertex?
is it 10?
well, if the distance from the vertex to the focus, is the exact same one as the distance from the vertex to the directrix
that means that the vertex is half-way between both of them
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see now where the vertex is?
yeap, is at the origin, 0, 0
notice the distance from the vertex to the focus (0, -10), is 10 units
the "focus form" for a parabola like so is \(\bf (x-h)^2=4p(y-k)\)
(h, k) = vertex coordinates
p = distance from the vertex to the focus point
so i just plug the numbers in? (0 - 0)^2 = 4(10) (-10 - 0)