The Whisper Room What does this have to do with ellipses?
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The Whisper Room
What does this have to do with ellipses?
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
B & B are called the endpoints of the minor axis.
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
F1F
2b
A1
A2
B1
B2
Oa
c
VERTICAL
ELLIPSE
Horizontal Ellipse Vertical Ellipse
ab
ca F1F2b
A1A 2
B1
B
The Pythagorean Property
b2 c2 a2+ =
b2c2 a2-=
Vertical EllipseHorizontal Ellipse
Constant
BY SYMMETRY
FOCAL RADII PROPERTY
Sketch each ellipse. Identify the length of the major and minor axes, the coordinates of the center, foci and vertices.
Sketch each ellipse. Identify the length of the major and minor axes, the coordinates of the center, foci and vertices.
From Standard to General Form and Back Again ...
Standard Form
General Form
Standard Form
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