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A parabola can be drawn given a focus of (-4, 4) and a directrix of y = –6. Write the equation of the parabola in any form.

 Mar 6, 2020
 #1
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The directrx  is  below the focus.....so this parabola turns upward

 

p =  the  distance  between  the  focus and directrix  / 2   =   (4 - - 6)  / 2  = 10 /2  = 5

 

So the  vertex =   ( - 4,  4 - p)   =  ( -4, 4 -5)  = (-4, -1)

 

So  we  have   this form

 

4p ( y - k)  =  (x - h)^2            where  (h, k)  is the vertex.......so....we have

 

4(5) ( y -  -1)   = ( x   + 4)^2      simplify

 

20 (y + 1)  = ( x + 4)^2

 

20y + 20   = x^2  + 8x  + 16       subtract  20 from both sides

 

20y =   x^2  + 8x   - 4      divide  both sides by 20

 

y = (1/20)x^2 + (2/5)x  - (1/5)

 

Here's the graph  :  https://www.desmos.com/calculator/5tzekvcuhj

 

 

 

cool cool cool

 Mar 6, 2020

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