Reorder the expression to get the standard form of a parabola #x = ay^2 +bxy+c#, which can then be reformed into vertex form as # 4p(x-h) = (y-k)^2#. From that the focus and directrix can be found from the standard expressions where #p# is the distance between the vertex and the focus, and also the distance from the vertex to the directrix.
#x = -(y^2 +y)#
#x = -(y+1/2)^2 + 1/4#
#(x-1/4) = -(y+1/2)^2#
The vertex is #(1/4,-1/2)#
The equation represents a horizontal parabola opening to the left.
#4p = 1# so #p=1/4#. The focus is#1/4# to the left of the vertex, so the focus is the point #(0,-1/2)#
The directrix is #p# to the right of the vertex so the directrix is #x = 1/2#
