pre-cal 40s may 21, 2009
DESCRIPTION
Introduction to the ellipse.TRANSCRIPT
The Whisper Room
What does this have to do with ellipses?
Generating Ellipses HOMEWORK
Drawing Ellipses
O
The Anatomy of The EllipseP
O is the centre.
aA1A 2 O
a
The Anatomy of The EllipseP
O is the centre.A A is the length of the major axis. It's length is 2a.
21
aF1F2
A1A 2 Oa
The Anatomy of The EllipseP
O is the centre.A A is the length of the major axis. It's length is 2a.
21
PF & PF are the focal radii of the ellipse.
21
ca
F1F2A1A 2 O
ac
The Anatomy of The EllipseP
O is the centre.A A is the length of the major axis. It's length is 2a.
21
OA = OA is the length of the semimajor axis with length a.
1 2
PF & PF are the focal radii of the ellipse.
21
ba
F1F2b
A1A 2
B1
B2
Oa
The Anatomy of The EllipseP
O is the centre.A A is the length of the major axis. It's length is 2a.
21
B B is the length of the minor axis. It's length is 2b.
21
OA = OA is the length of the semimajor axis with length a.
1 2
PF & PF are the focal radii of the ellipse.
21
ba
F1F2b
A1A 2
B1
B2
Oa
The Anatomy of The EllipseP
O is the centre.A A is the length of the major axis. It's length is 2a.
21
B B is the length of the minor axis. It's length is 2b.
21
OA = OA is the length of the semimajor axis with length a.
1 2
OB = OB is the length of the semiminor axis with length b.
1 2
PF & PF are the focal radii of the ellipse.
21
b
ca
F1F2b
A1A 2
B1
B2
Oa
c
The Anatomy of The EllipseP
O is the centre.A A is the length of the major axis. It's length is 2a.
21
B B is the length of the minor axis. It's length is 2b.
21
OA = OA is the length of the semimajor axis with length a.
1 2
OB = OB is the length of the semiminor axis with length b.
1 2
PF & PF are the focal radii of the ellipse.
21 F & F are called the foci. They are c units from the centre.
21
b
ca
F1F2b
A1A 2
B1
B2
Oa
c
The Anatomy of The EllipseP
O is the centre.A A is the length of the major axis. It's length is 2a.
21
B B is the length of the minor axis. It's length is 2b.
21
OA = OA is the length of the semimajor axis with length a.
1 2
OB = OB is the length of the semiminor axis with length b.
1 2
A & A are called the vertices of the ellipse.
21
PF & PF are the focal radii of the ellipse.
21 F & F are called the foci. They are c units from the centre.
21
b
ca
F1F2b
A1A 2
B1
B2
Oa
c
The Anatomy of The EllipseP
O is the centre.A A is the length of the major axis. It's length is 2a.
21
B B is the length of the minor axis. It's length is 2b.
21
OA = OA is the length of the semimajor axis with length a.
1 2
OB = OB is the length of the semiminor axis with length b.
1 2
A & A are called the vertices of the ellipse.
21
PF & PF are the focal radii of the ellipse.
21 F & F are called the foci. They are c units from the centre.
21
B & B are called the endpoints of the minor axis.
21
b
ca
F1F
2b
A1
A2
B1
B2
Oa
c
VERTICAL
ELLIPSE
ab
ca F1F2b
A1A 2
B1
B
The Pythagorean Property
b2 c2 a2+ =
b2c2 a2-=
Vertical EllipseHorizontal Ellipse
Horizontal Ellipse Vertical Ellipse
Generating Hyperbolas HOMEWORK