SOLUTION: Find an equation for the parabola with focus (4,6) and directrix on the x-axis.

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Question 1140354: Find an equation for the parabola with focus (4,6) and directrix on the x-axis.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
points (4,6) and (x,0)
Focus and Directrix

%28x-4%29%5E2%2B%28y-6%29%5E2=%28x-x%29%5E2%2B%28y-0%29%5E2 from Distance Formula and definition for parabola


%28x-4%29%5E2%2By%5E2-12y%2B36=y%5E2
x%5E2-8x%2B16=12y-36
highlight%28%28x-4%29%5E2=12%28y-3%29%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Focus (4,6) and directrix y=0 means the vertex is (4,3); the parabola opens upward.

The general form of the equation of a parabola with vertex (h,k) that opens up or down is

%28y-k%29+=+%281%2F%284p%29%29%28x-h%29%5E2

where p is the directed distance from the vertex to the focus; for this example, p=3. Then the formula for this parabola is

%28y-3%29+=+%281%2F12%29%28x-4%29%5E2