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Warm-Up 1/09

Warm-Up 1/09. 1. 2. B. G. Rigor: You will learn how to identify, analyze and graph equations of ellipses and circles , and how to write equations of ellipses and circles. Relevance: You will be able to use graphs and equations of ellipses and circles to solve real world problems.

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Warm-Up 1/09

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  1. Warm-Up 1/09 1. 2. B G

  2. Rigor:You will learn how to identify, analyze and graph equations of ellipses and circles, and how to write equations of ellipses and circles.Relevance:You will be able to use graphs and equations of ellipses and circles to solve real world problems.

  3. 7-2 Ellipses and Circles

  4. 2b 2c 2a

  5. Example 1: Graph the ellipse given by the equation. Orientation: horizontal Center : foci: and vertices: and co-vertices: • major axis : • • • F F• • minor axis : •

  6. Example 2a: Write an equation for an ellipse with given characteristics. major axis from (– 6, 2) to (– 6, – 8); minor axis from (– 3, – 3) to (– 9, – 3) Orientation: vertical 3 Center

  7. Example 2b: Write an equation for an ellipse with given characteristics. vertices at(– 4, 4) and (6, 4); foci at (– 2, 4) and (4, 4) Orientation: horizontal Center

  8. Example 3: Determine the eccentricity of the ellipse given by . The eccentricity is about 0.95, so the ellipse will appear stretched.

  9. Example 5a: Write the equation in standard form. Identify the related conic. The conic section is a parabola with vertex (3, – 2).

  10. Example 5b: Write the equation in standard form. Identify the related conic. The conic section is a circle with center (6, – 5) and radius 7.

  11. Example 5c: Write the equation in standard form. Identify the related conic. The conic section is an ellipse with center (3, 0).

  12. math! • 7-2 Assignment: TX p438, 4-36 EOE + 34

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