The document discusses the anatomy and key properties of ellipses. It defines the major axis, minor axis, foci, vertices, and center of an ellipse. It also examines the differences between horizontal and vertical ellipses and explores the Pythagorean property and focal radii property of ellipses. Diagrams and equations are provided to illustrate these concepts.

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

5. 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 B1 B2 is the length of the
major axis. It's length is 2a. minor axis. It's length is 2b.
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.
OB1 = OB2 is the length of the B1 & B 2 are called the
semiminor axis with length b. endpoints of the minor axis.

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

7. Horizontal Ellipse Vertical Ellipse

8. 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

9. FOCAL RADII PROPERTY
Constant
BY SYMMETRY

10. Sketch each ellipse. Identify the length of the major and minor axes,
the coordinates of the center, foci and vertices.

11. Sketch each ellipse. Identify the length of the major and minor axes,
the coordinates of the center, foci and vertices.

12. From Standard to General
Form and Back Again ...
Standard Form
General Form
Standard Form