What are the focus and directrix of the parabola with the given equation?
x = -1/8 y^2
The given equation is in the form x = ay^2, which is the standard equation of a parabola that opens horizontally.
The focus of the parabola is located at (a,0), where 4a is the coefficient of y^2 in the equation.
In this case, 4a = -1/8, so a = -1/32.
Therefore, the focus of the parabola is at (-1/32, 0).
The directrix of the parabola is a vertical line given by the equation x = -a.
In this case, the directrix is x = 1/32.
So, the focus of the parabola is (-1/32, 0) and the directrix is x = 1/32.