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.

Option C.

Step-by-step 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.