Answer: Choice A
Explanation:
We can eliminate choices B, C and D for the following reasons
- B) The set of points equally distant from a center makes up a circle, and not a parabola.
- C) The vertex point is 0 units away from the axis of symmetry, but the distance from the vertex to the focus is nonzero. This is one example showing we don't have the distances matching up.
- D) A straight line is the locus of points equally distant from two other points. More specifically, the perpendicular bisector is what this locus of points makes up.
Choice A is the only thing left. It turns out that any point on the parabola is equally distant from the focus to the directrix. The directrix is perpendicular to the axis of symmetry. The distance from the vertex to the directrix is the same distance as the focal length.
