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Subject: "Focus of parabola."     Previous Topic | Next Topic
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Conferences The CTK Exchange College math Topic #527
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Ganitopasak
guest
Aug-27-05, 07:40 PM (EST)
 
"Focus of parabola."
 
   Hello,

How to calculate the focus of parabola given by:

(x 3)^2 = (y + 1)

Thanks for any help.


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delta59
guest
Aug-29-05, 07:27 AM (EST)
 
1. "RE: Focus of parabola."
In response to message #0
 
   The vertex of any parabola lies on the axis of symmetry and is equidistant from the focus and the directrice. In your case the vertex is V(3,-1). Assume focus F has coordinates F(3,-1+t) so directrice has equation y = -1 t. Find any point on the parabola, for example A(2,0).
Then AF^^2 = (2-3)^^2 + (0-(-1+t))^^2 = t^^2 2t + 2. And the distance from A to the directrice is t+1. So (t+1)^^2 = t^^2 2t + 2 .This gives t = 1/4.


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