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Question 715317: I basically have a general question. I am trying to use information provided to write the transformational equation of each parabola. I am given the vertex and focus and the vertex and directrix. I know how to find p but I do not where to put it and when the x is squared vs the y being squared. I guess I need the rules?
Example: Vertex: (-7,-8) Focus: (47/8,8)
Knowing that the Vertex is (h,k)...
I take the absolute value of 6-(47/8)=(1/8)... (1/8) is the value of p
4*(1/8)= .5
After that I am lost...
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I basically have a general question. I am trying to use information provided to write the transformational equation of each parabola. I am given the vertex and focus and the vertex and directrix. I know how to find p but I do not where to put it and when the x is squared vs the y being squared. I guess I need the rules?
Example: Vertex: (6,8) Focus: (47/8,8)
Knowing that the Vertex is (h,k)...
I take the absolute value of 6-(47/8)=(1/8)... (1/8) is the value of p
4*(1/8)= .5
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Rules:
In the form 4p(y-k) = (x-h)^2 the vertex is (h,k)
If "4p" is positive the parabola opens up.
If "4p" is negative the parabola opens down.
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"P" is the distance from the vertex to the focus
AND
"p" is the distance from the vertex to the directrix.
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In the form 4p(x-h) = (y-k)^2 the vertex is (h,k)
If "4p" is positive the parabola opens to the right
If "4p" is negative the parabola opens to the left.
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Your Problem:
Vertex at (6,8) so h = 6 and k = 8
p = 1/8, so 4p = 1/2
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Since the vertex and the focus have the same y-value
the axis of symmetry is a y-line, or is horizontal.
Note: Notice that the focus is 1/8 to the left of the vertex,
so your parabola must be opening to the left.
Since the focus is to the left of the vertex, p is negative,
so 4p is negative.
(-1/2)(x-6) = (y-8)^2
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The directrix is |p| to the right the vertex:
x = 6 1/8
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Cheers,
Stan H.
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