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What is the equation of a parabola with  (4, 6) as its focus and y = 2 as its directrix  

angry

CrazyDaizy  Jun 2, 2017
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Whenever the focus lies above the directrix, the parabola turns "upward"

 

The  vertex  is  

( x coordinate of the focus, [sum of y coordinate of the focus + numerical value of the directrix]/ 2 )  =   ( 4,  [6 + 2] / 2 )  =  ( 4, 8/2)  =  (4, 4)

 

And we have the following form :

 

4p ( y - k)  =  (x - h)^2      where   (h, k)  is the vertex  and  "p"  =  y coordinate of the focus - y coordinate of the vertex  =  6 - 4  =   2

 

So we have

 

4(2) ( y - 4)  =  ( x - 4)^2

 

8 (y - 4)  =  ( x - 4)^2

 

See the graph, here ;

 

https://www.desmos.com/calculator/o8jsbrmpgz

 

 

cool cool cool

CPhill  Jun 2, 2017
edited by CPhill  Jun 2, 2017
edited by CPhill  Jun 2, 2017

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