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Write an equation of a parabola with focus of (1,3) and directrix y = 5. show work

Guest Mar 29, 2018
edited by Guest  Mar 29, 2018
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The directrix  is 8  units below the focus

So...the vertex  is  ( 2, (6 + -2)/2 )  =  (2, 4/2) =  (2, 2)

And  p  is the distance between the vertex  and directrix  =  [2 - (-2)]  =  4

 

So....we have the form

 

4p(y - k)  = (x  - h)^2       where  (h, k) is the vertex  and p  = 4

 

So  we have

 

4(4)(y - 2)  = (x - 2)^2

 

16 (y - 2)  = (x - 2)^2

 

(y - 2)  = (1/16)(x - 2)^2

 

y  =  (1/16)(x - 2) + 2

 

 

cool cool cool

CPhill  Mar 29, 2018
edited by CPhill  Mar 29, 2018

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