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avatar+555 

what are the vertex,focus and directrix of a parabola with equation \(x=-4y^2\)

how do i find this

and who ate my burrito

OfficialBubbleTanks  Mar 12, 2018
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3+0 Answers

 #1
avatar+86528 
+1

Can't answer the second one....but....for the first

 

The vertex  is (0,0)

This parabola opens to the left

 

The general form  for this type of parabola with the vertex is at the origin  is

 

-4px  = y^2         where p is the distance between the focus and the vertex

 

So....we have

 

x =  -4y^2        divide both sides by -4

 

(-1/4)x  = y^2

 

So.......this implies that  (-1/4) = -4p  ⇒  p = 1/16

 

So.....the focus in this situation is given by

 

(0 - p , 0)  =  (0 - 1/16 , 0 )  =  (-1/16, 0 )

 

And the directrix  is give by:    x = 1/16

 

Here's a graph :  https://www.desmos.com/calculator/z66mdaucdo 

 

cool cool cool

CPhill  Mar 12, 2018
 #2
avatar+555 
+1

you answered the second by answering the first one :D

OfficialBubbleTanks  Mar 12, 2018
 #3
avatar+86528 
0

LOL!!!!

 

 

cool cool cool

CPhill  Mar 12, 2018

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