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Question 870783: Please help....I cannot help my son with this question.
What is the equation of the quadratic graph with a focus of (6,0) and a directrix of y=-10?
Please explain, if possible how to work this kind of a problem. Thank you so much!!!
Found 2 solutions by josgarithmetic, ewatrrr:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! Try to use something (relatively) simple, like a parabola. He would or should use the Distance Formula according to the definition of a parabola.
The directrix as given, means that this directrix is the set of points (x, -10), meaning y=-10 and x is any and all real values, this is a horizontal line with the constant value of -10.
Create the equation based on this:
The distance between the variable set of points (x,y) and F is equal to the distance between the set of points (x,-10) and the variable set of points (x,y).
After forming this equation, simplify it until it is in a form  . Try drawing a picture or graph, because this will greatly help.
More help possible if needed - but drawing the picture through this online system is not so easy or fast.
Answer by ewatrrr(24785)  (Show Source):
You can put this solution on YOUR website!
Hi
Horizontal Directrix: y = -10, Parabola Opens Upward (Focus above it)
F(6,0)
(0-10)/2 = -5 V(6, -5), p = 5
y = (1/4p)(x - 6)^2 - 5
y = (1/20)(x - 6)^2 - 5
the vertex form of a Parabola opening up(a>0) or down(a<0), 
where(h,k) is the vertex and x = h is the Line of Symmetry. a = 1/4p
where the focus is (h,k + p)
With Directrix y = (k - p)
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