How do you find the vertex, focus and directrix of x+y^2=0?

1 Answer
Aug 3, 2018

Vertex is at (0,0), focus is at (-0.25,0) and
directrix is
x= 0.25

Explanation:

x+y^2=0 or y^2 = -x or (y-0)^2 = -4 *1/4 (x-0)

The equation of horizontal parabola opening left is

(y-k)^2 = -4 p(x-h) ; h=0 ,k=0 ; p= 1/4=0.25

Therefore, vertex is at (0,0) The distance between focus and

vertex is p=0.25 :. Focus is at (-0.25,0) . Vertex is at midway

between focus and directrix. Therefore , directrix is x= 0.25

graph{x+y^2=0 [-12.66, 12.65, -6.33, 6.33]} [Ans]