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 _____________!