Solving Quadratic Inequalities October 9, 2015 SWBAT: Solve Quadratic Inequalities.
Chapter 9: Quadratic Relations and Systems Section 9-3: Ellipses.
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Transcript of Chapter 9: Quadratic Relations and Systems Section 9-3: Ellipses.
![Page 1: Chapter 9: Quadratic Relations and Systems Section 9-3: Ellipses.](https://reader035.fdocuments.us/reader035/viewer/2022072110/56649f0b5503460f94c1ea48/html5/thumbnails/1.jpg)
Chapter 9:Quadratic Relations
and Systems
Section 9-3: Ellipses
![Page 2: Chapter 9: Quadratic Relations and Systems Section 9-3: Ellipses.](https://reader035.fdocuments.us/reader035/viewer/2022072110/56649f0b5503460f94c1ea48/html5/thumbnails/2.jpg)
Objectives:Given the equation of an ellipse:
Sketch the graph
Calculate the focal radii and plot the foci
Check the sketch by computer graphics
![Page 3: Chapter 9: Quadratic Relations and Systems Section 9-3: Ellipses.](https://reader035.fdocuments.us/reader035/viewer/2022072110/56649f0b5503460f94c1ea48/html5/thumbnails/3.jpg)
EllipseAn ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then back to the other focal point has the same length for every point on the curve.
![Page 4: Chapter 9: Quadratic Relations and Systems Section 9-3: Ellipses.](https://reader035.fdocuments.us/reader035/viewer/2022072110/56649f0b5503460f94c1ea48/html5/thumbnails/4.jpg)
Graph of an Ellipse
![Page 5: Chapter 9: Quadratic Relations and Systems Section 9-3: Ellipses.](https://reader035.fdocuments.us/reader035/viewer/2022072110/56649f0b5503460f94c1ea48/html5/thumbnails/5.jpg)
X-Radius and Y-RadiusIf an ellipse has its major and minor axes parallel to the coordinate axes, then:
The x-radius is the distance from the center to the ellipse in the x-direction.
The y-radius is the distance from the center to the ellipse in the y-direction
![Page 6: Chapter 9: Quadratic Relations and Systems Section 9-3: Ellipses.](https://reader035.fdocuments.us/reader035/viewer/2022072110/56649f0b5503460f94c1ea48/html5/thumbnails/6.jpg)
Equation for an Ellipse
22
1x y
x h y k
r r
![Page 7: Chapter 9: Quadratic Relations and Systems Section 9-3: Ellipses.](https://reader035.fdocuments.us/reader035/viewer/2022072110/56649f0b5503460f94c1ea48/html5/thumbnails/7.jpg)
Example 1:Sketch the graph of:
2 225 9 200 18 184 0x y x y
![Page 8: Chapter 9: Quadratic Relations and Systems Section 9-3: Ellipses.](https://reader035.fdocuments.us/reader035/viewer/2022072110/56649f0b5503460f94c1ea48/html5/thumbnails/8.jpg)
HOMEWORK
p. 476 #1-15 odd