Consider the parabola represented by the equation -2y2 = 4x.
this parabola will open to the ?
.
the equation of the directrix of the parabola is ?
.
the focus of the parabola is ?
.

The given expression is

If we rewrite this expression, it would be

Or, we can rewrite this way too

As you can observe, the quadratic variable is not , this change the orientation of the figure. Actually, this change a lot, because this parabola doesn't represent a function, because it will open horizontally, specifically, towards negative infinte, like the image attached shows.

If you do the vertical line test, you will see that such vertical line intercepts the figure in two points, which indicates that it's not a function.

Now, in this case, the directrix is defined as , because the parabola is horizontal. Where is the horizontal coordinate of the vertex, and can be found as follows.

When, the parabola is horizontal is defined as

Where are the coordinates of the vertex, which in this case is . Also, particularly, we have that

So,

Then, the directrix would be

And the focus is defined as