9514 1404 393
Answer:
B. F(-9/2, 0), x = 9/2
Explanation:
One definition of a parabola is that it is all of the points that are equidistant from the focus and the directrix. Among other things, this means the parabola "wraps around" the focus, and opens away from the directrix.
The focus is on the axis of symmetry, so shares a coordinate with the vertex. Since the vertex is a point on the parabola, it is equidistant from the focus and directrix—halfway between them.
The given equation has x get more negative as y increases, so the parabola opens to the left. This means the focus will be a point on the -x axis. Only one answer choice meets that requirement:
focus: (-9/2, 0), directrix: x = 9/2
__
The equation of a parabola with its vertex at the origin can be written as ...
x = 1/(4p)y^2
In this case, we have 4p = -18, so p = -9/2. This is the distance from the vertex to the focus. The negative sign means the focus is to the left of the vertex, and its x-coordinate is -9/2 (as noted above).