Pre-Cal 40S Slides May 13, 2008
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Transcript of Pre-Cal 40S Slides May 13, 2008
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The Whisper Room
What does this have to do with ellipses?
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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
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b
ca
F1F
2b
A1
A2
B1
B2
Oa
c
VERTICAL
ELLIPSE
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Horizontal Ellipse Vertical Ellipse
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ab
ca F1F2b
A1A 2
B1
B
The Pythagorean Property
b2 c2 a2+ =
b2c2 a2-=
Vertical EllipseHorizontal Ellipse
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Constant
BY SYMMETRY
FOCAL RADII PROPERTY
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Sketch each ellipse. Identify the length of the major and minor axes, the coordinates of the center, foci and vertices.
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Sketch each ellipse. Identify the length of the major and minor axes, the coordinates of the center, foci and vertices.
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From Standard to General Form and Back Again ...
Standard Form
General Form
Standard Form