what are the focus and directrix of the parabola with the given equation x=-1/8y^2
The given equation x = -1/8y^2 can be rewritten in standard form as y^2 = -8x.
Now we can identify that the focus of the parabola is a point (h, k) where h = -1/2a and the directrix is a vertical line x = h - 1/(4a).
In this case, a = -1/8, so h = -1/(2*(-1/8)) = 4 and the focus is at (4, 0).
The directrix is the vertical line x = 4 - 1/(4*(-1/8)) = 4 - 2 = 2.
Therefore, the focus of the parabola is at (4, 0) and the directrix is the line x = 2.