Hyperbola (Locus Construction)
- Author:
- Tim Brzezinski
- Topic:
- Hyperbola
In this diagram,
Line p is the perpendicular bisector of CD.
Point C is a point on circle with center A.
Point H_1 is the intersection of p and ray 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 (AH_1 – CH_1) is _________________.
Since H_1 lies on p (the perpendicular bisector of DC) , we know ____ = ______. Why is this?
Since (AH_1 – CH_1) is ______________, and since CH_1 = ______, it also must be true that the quantity
AH_1 – _____ is CONSTANT as well, regardless of where point H_1 lies.
This implies that point H_1 is guaranteed to lie on one branch of a/an _______________________with points A and D serving as its __________!