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Write the equation of a parabola with focus (2,2) and directrix y = -4.

 Nov 17, 2020
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focus = ( 2,2)

directix = y =  -4

 

The directrix is below the  fosus so this parabola will turn upward

 

The form we are  looking  for is

 

4p ( y - k)  = (x - h)^2

 

(h , k) is the  vertex   .....this is  given  by  ( x coordinate of focus , ( y coordinate of focus + directrix) / 2)  =

(2 , ( 2 +-4) / 2)  =  ( 2 ,-2/2)  =   (2, -1)

 

p =  the distance  between the fcus and the  vertex = y coordinate of focus  -  y  coordinate  of  vertex  =

2 - -1  =   3

 

So....the equation is

 

4(3) ( y - - 1) = ( x -2)^2   →    12 (y + 1) = ( x - 2)^2

 

Here's the graph  :  https://www.desmos.com/calculator/xik9fowbq0

 

 

cool cool cool

 Nov 17, 2020

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