The document discusses the key elements that define an ellipse: - The ellipse has a center point O. - It has a major axis A1A2 of length 2a and a minor axis B1B2 of length 2b. - There are two focal points, F1 and F2, located a distance c from the center. - The sum of the distances from any point on the ellipse to the two focal points is a constant, equal to 2a.

1. The Whisper Room
What does this have
to do with ellipses?

2. Generating Ellipses HOMEWORK

3. Drawing Ellipses

4. The Anatomy of The Ellipse
P
O
O is the centre.

5. The Anatomy of The Ellipse
P
a a
A2 A1
O
O is the centre.
A1A2 is the length of the
major axis. It's length is 2a.

6. The Anatomy of The Ellipse
P
a a
A2 A1
F2 O F1
O is the centre.
A1A2 is the length of the
major axis. It's length is 2a.
PF1 & PF 2 are the focal
radii of the ellipse.

7. The Anatomy of The Ellipse
P
a a
A2 c A1
F2 O c F1
O is the centre.
A1A2 is the length of the
major axis. It's length is 2a.
PF1 & PF 2 are the focal
radii of the ellipse.
OA1 = OA2 is the length of the
semimajor axis with length a.

8. The Anatomy of The Ellipse
B1 P
b
a a
A2 A1
F2 O F1
b
O is the centre. B2
A1A2 is the length of the
major axis. It's length is 2a.
PF1 & PF 2 are the focal
radii of the ellipse.
OA1 = OA2 is the length of the
semimajor axis with length a.
B1 B2 is the length of the
minor axis. It's length is 2b.

9. The Anatomy of The Ellipse
B1 P
b
a a
A2 A1
F2 O F1
b
O is the centre. B2
A1A2 is the length of the OB1 = OB2 is the length of the
major axis. It's length is 2a. semiminor axis with length b.
PF1 & PF 2 are the focal
radii of the ellipse.
OA1 = OA2 is the length of the
semimajor axis with length a.
B1 B2 is the length of the
minor axis. It's length is 2b.

10. The Anatomy of The Ellipse
B1 P
b
a a
A2 c A1
F2 O c F1
b
O is the centre. B2
A1A2 is the length of the OB1 = OB2 is the length of the
major axis. It's length is 2a. semiminor axis with length b.
PF1 & PF 2 are the focal F 1 & F 2 are called the foci. They
radii of the ellipse. are c units from the centre.
OA1 = OA2 is the length of the
semimajor axis with length a.
B1 B2 is the length of the
minor axis. It's length is 2b.

11. The Anatomy of The Ellipse
B1 P
b
a a
A2 c A1
F2 O c F1
b
O is the centre. B2
A1A2 is the length of the OB1 = OB2 is the length of the
major axis. It's length is 2a. semiminor axis with length b.
PF1 & PF 2 are the focal F 1 & F 2 are called the foci. They
radii of the ellipse. are c units from the centre.
OA1 = OA2 is the length of the A1 & A 2 are called the
semimajor axis with length a. vertices of the ellipse.
B1 B2 is the length of the
minor axis. It's length is 2b.

12. The Anatomy of The Ellipse
B1 P
b
a a
A2 c A1
F2 O c F1
b
O is the centre. B2
A1A2 is the length of the OB1 = OB2 is the length of the
major axis. It's length is 2a. semiminor axis with length b.
PF1 & PF 2 are the focal F 1 & F 2 are called the foci. They
radii of the ellipse. are c units from the centre.
OA1 = OA2 is the length of the A1 & A 2 are called the
semimajor axis with length a. vertices of the ellipse.
B1 B2 is the length of the B1 & B 2 are called the
minor axis. It's length is 2b. endpoints of the minor axis.

13. ELLIPSE
VERTICAL
B1
b
A1 a a A2
F1 c O c F2
b
B2

15. The Pythagorean Property
B1
a
b
A2 a A1
F2 c F1
b 2 2
b+ c = a2
B
2 2 2
c =a - b
Horizontal Ellipse Vertical Ellipse

17. Horizontal Ellipse Vertical Ellipse

18. Generating Hyperbolas HOMEWORK