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

#1**+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

CPhill
Mar 12, 2018