pre-cal 40s slides december 13, 2007
DESCRIPTION
More on the ellipse.TRANSCRIPT
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The Whisper Room
What does this have to do with ellipses?
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b
c
a
F1F2b
A1A2
B1
B2
Oa
c
The Anatomy of The Ellipse
O is the CENTRE
P
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ab
ca F1F2b
A1A2
B1
B
The Pythagorean Property
b2 c2 a2+ =
b2c2 a2 -=
Vertical EllipseHorizontal Ellipse
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Horizontal Ellipse Vertical 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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A parabola has vertex (0, 0) and focus on a coordinate axis. Write the equation of the parabola if:
(b) the directrix is defined by the line y = 8.
(a) the focus is: (i) (4, 0) (ii) (-6, 0) (iii) (0, 3)
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For each ellipse whose equation is given below
(i) Write the equation in standard form(ii) Determine the lengths of the major and minor axes, the coordinates
of the verticies, and the coordinates of the foci.(iii) Sketch a graph of the ellipse.
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