Chapter 8.1, Problem 65E

Solution

To State with justification:

Whether the given statement is true or false.

False according to the definition of the parabola as the locus of the point whose distance from a particular point called focus remains equal to its distance from a particular line called directrix.

Given:

The statement: “Every point on a parabola is the same distance from its focus and its axis.”

Explanation:

A parabola is the locus of the point whose distance from a particular point called focus remains equal to its distance from a particular line called directrix.

By definition, every point on a parabola is the same distance from its focus and its directrix.

Conclusion:

Every point on a parabola is the same distance from its focus and its directrix, not its axis. The given statement is false.