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Question 409739: Can you please help with the following question?
Write an equation of a parabola with the vertex at the origin and directrix at y=6
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Write an equation of a parabola with the vertex at the origin and directrix at y=6
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With the given information we are looking at a parabola with the form: (x-h)^2=4p(y-k), with (h,k) being the (x,y) coordinates of the vertex.
Since the vertex is at the origin, this equation becomes: x^2=4py
The parabola always curves away from the directrix, y=6, so it goes downward making the coefficient of x^2 negative, that is, -x^2=4py or x^2=-4py
Since the directrix is 6 or P units above the vertex on the axis of symmetry, x=0,the focus is likewise 6 or P units below the vertex. Therefore,p=6.
The final equation is now x^2=-4*6y=-24y or x^2=-24y
See the graph of this equation below: (The green line is the directrix, y=6)
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