+577 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
+129849 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
