Question

Which of the following best describes the relationship between the focus and directrix of a parabola?

A. The focus is half the distance from the parabola as the directrix.
B. The focus is twice the distance from the parabola as the directrix.
C. They are equidistant from the parabola.
D. They both lie on the graph of the parabola.

Answer 1

Option C.

Explanation:

If a point (x, y) lie on a parabola then distance from this point to the focus is always equal to it's distance from the directrix.

We can see in the picture attached, Point P is any point on parabola having coordinates (x, y).

A is the focus and directrix is the line passing through point B and parallel to x axis.

Therefore distance from point P will be PA = PB which matches the option C.

Answer 2

A parabola is the set of all points in a plane that are equidistant from a fixed line and from a fixed point. Focus is the point from which all points on the parabola have same distance and directix is the line. The distance between a point (x,y) on the parabola and the focus is the same as the distance between the point (x,y) and the directix.So, the following statement about the relationship between the focus and directrix of a parabolathe is true:
C. They are equidistant from the parabola.