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2.) Explain how to find the coordinates of the focus of a parabola with vertex (0,0) and directrix y = 5.

 Feb 19, 2019
 #1
avatar+100439 
+3

The parabola opens downward because the directrix is above the vertex.....to find the focus we have

 

( x coordinate of the vertex,  y coordinate of the vertex - y value of the directrix ) = 

 

(0, 0 - the y value of the directrix)  =

 

(0 , 0 - 5 )  =

 

(0 , - 5)  =   the focus

 

cool cool cool

 Feb 19, 2019
 #2
avatar+100439 
+3

As as alternative way to do this....note that the distance between the vertex and directrix = 5 units = "p"

 

Since the directrix is above the vertex....the coordinates of the focus =

 

( x coordinate of the vertex, y coordinate of the vertex - p )  =

 

(0 , 0 - 5 ) =

 

(0, - 5)

 

 

cool cool cool

CPhill  Feb 19, 2019

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