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Chapter 6: Problem 77

Determine whether the statement is true or false. Justify your answer. It is possible for a parabola to intersect its directrix.

Short Answer

Expert verified
The statement is false. A parabola does not intersect its directrix by definition because a parabola is the set of all points that are equidistant from a focus point and a line (the directrix).

Step by step solution

01

Understanding the Elements of a Parabola

A parabola is a set of all points that are equidistant from a point that is called the focus, denoted by (h,k), and a line, referred to as the directrix, often represented as y=mx+b.
02

Determining Intersection

The geometrical definition of a parabola in itself provides the clue to the answer. Since a parabola is a set of all points that are equidistant from a focus point and a line (directrix), the parabola never intersects its directrix.
03

Final Conclusion

The claim that 'a parabola can intersect its directrix' is therefore false. The nature of a parabola, by definition, indicates that it never intersects its directrix.

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Most popular questions from this chapter

In Exercises \(71-90,\) convert the rectangular equation to polar form. Assume \(a > 0\). $$x y=16$$

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