Ellipse (Locus Construction)

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 _____________!