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Find the focus and directrix for each parabola below:

 Mar 6, 2019
 #1
avatar+100546 
+2

a)    y = -(1/8) ( x + 3)^2 - 2

 

The vertex is (-3, -2)

The parabola turns downward

 

In this form

 

(1/8) =   1/[4p]    so     p   =  2

 

The focus is    (-3, -2 - p)  =  (-3 , - 2 - 2)  =  (-3, -4)

 

The directrix  is  y  =  -2 + p  =  -2 + 2  = 0   

 

 

b )    4y = x^2 - 20

 

4y + 20  = x^2

 

4 ( y + 5) = (x - 0)^2

 

The vertex is  (0, -5)   and the parabola turns upward

 

In this form

 

4p = 4  ⇒  p = 1

 

The focus is   (0, -5 + p) =  ( 0, -5 + 1)   = (0, -4)

 

The directrix is

 

y =  -5 - p =  -5 - 1  = -6

 

 

 

cool cool cool

 Mar 6, 2019

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