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Which equation represents a parabola that has a focus of (0, 0) and a directrix of y = 4?

x^2=−8y

x^2=−8(y−2)

x^2=−2(y−2) ​

x^2=−2y

 Feb 6, 2019
edited by jjennylove  Feb 6, 2019
 #1
avatar+98129 
+2

If the directri is y = 4   and the focus is (0,0).....the vertex = (0, (0 + 4)/2 )  = (0, 2  )= (h, k)

 

In other words....the vertex is midway between the focus and the directrix

 

p  is the distance between the vertex and the focus = 2

 

And since the directrix is above the focus, the parabola opens downward

 

And we have the form

 

-4p ( y - k) = x^2

 

-4p(y-2) = x^2                (we use the " - " because the parabola opens downward )

 

- 4(2) (y -2) = x^2

 

-8(y - 2) = x^2

 

EDIT TO CORRECT AN ERROR

 

cool cool cool

 Feb 6, 2019
edited by CPhill  Feb 6, 2019
 #2
avatar+708 
+1

oh okay! That makes more sense . Thank you smiley

jjennylove  Feb 6, 2019
 #3
avatar+708 
0

This one actually ended up being incorrect

jjennylove  Feb 6, 2019
 #4
avatar+98129 
+1

Oops....sorry Jenny...fixed it...

 

cool cool cool

CPhill  Feb 6, 2019
 #5
avatar+708 
0

Its okay smiley

jjennylove  Feb 6, 2019

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