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Given the focus of the parabola (0,-6), and the directirx y=6, find the equation of the parabola.
Since the focus is below the directrix on the axis of symmetry,(x=0), this is a parabola which opens downward. Its standard form of equation: (x-h)^2=-4p(y-k), (h,k) being the (x,y) coordinates of the vertex:
For given parabola:
y-coordinate of vertex=half-way between directrix and focus on axis of symmetry=0
x-coordinate of vertex=0
p=distance from vertex to focus or to directrix on the axis of symmetry=6
Equation of given parabola: