# Ellipse (Locus Construction)

- Author:
- Tim Brzezinski

- Topic:
- Ellipse

In this diagram,
Line p is the perpendicular bisector of DC.
Point C is a point on circle with center A.
Point E is the intersection of p and radius AC.

**Directions:**Fill in the blanks below: Since the radius of any circle never changes, it is said to be _______________________. This implies radius AC is _______________________. This also means means (AE + EC) is _______________________. Since E lies on p (the perpendicular bisector of DC , we know ___ = ____.

*Why is this?*Since (AE + EC) is ____________________, and since EC = ____________________, it also must be true that the quantity AE + _____ is CONSTANT, regardless of where point E lies. This implies that point E is guaranteed to lie on a/an ___________________ with points A and D serving as its _____________!