conic sections part 2: ellipses integrated math 4 mrs. tyrpak
TRANSCRIPT
![Page 1: Conic Sections Part 2: Ellipses Integrated Math 4 Mrs. Tyrpak](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f2b5503460f94c4520f/html5/thumbnails/1.jpg)
Conic Sections Part 2:Ellipses
Integrated Math 4
Mrs. Tyrpak
![Page 2: Conic Sections Part 2: Ellipses Integrated Math 4 Mrs. Tyrpak](https://reader035.vdocuments.net/reader035/viewer/2022062722/56649f2b5503460f94c4520f/html5/thumbnails/2.jpg)
Ellipses
The parametric equations for ellipses:
What are the x-intercepts and y-intercepts of the ellipse?
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Horizontal and Vertical Axes
What is the length of both axes in both Graphs?
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Major and Minor Axes
The longer axis of an ellipse is the ________ axis, and the shorter is the
________ axis.
When will the horizontal axis of an ellipse be the major axis? The minor axis?___________________________
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Eliminate the parameter
This will produce a rectangular equation for an ellipse.
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Standard form for an Ellipse
Center (h,k)
Horizontal Axis: 2a
Vertical Axis: 2b
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Using Standard Form
Write in standard form the equation of an ellipse with center (3, -5), horizontal axis length 12 and vertical axis length 20.
Write in expanded form
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Expanded Form Standard
Write the following in standard form
and describe the nature of the graph.
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You try one…
Write the following in standard form and describe the nature of the graph.
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Secondary definition for an ellipse:
It is a set of points in a plane for which the sum of the distances from two fixed points, called the foci, is a constant.
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General Case Explanation
Suppose the foci are , and that for any point P, the sum of the distances to the foci is 2a where
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Explain the following:
1. Why the x-intercepts are (-a,0) and (a,0)
2. Why the y-intercepts are (0, -b) and (0, b), where
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You know what I’m going to say!
Awesome job!!
Don’t forget to complete your extension and enrichment worksheets before you
move on.
Remember you are a mathematician