How do you find the focus, vertex, and directrix of #x = -6y^2#?

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Answer 1 · 2018-05-08T12:59:34

Vertex is at # (0,0)#, focus is at #(-1/24,0) #
and directrix is # x = 1/24#

# x = - 6 y^2 or y^2 = - x/6 or y ^2 = -4 *1/24 x#

The equation of horizontal parabola opening left is

#(y-k)^2 = -4 a(x-h) ; h=0 ,k=0 , a = 1/24#

Vertex is at #(h,k) or (0,0)#

Focus is at #(-a,0) or (-1/24,0) #

Directrix is # x = a or x = 1/24#

graph{x= -6 y^2 [-12.66, 12.65, -6.33, 6.33]} [Ans]