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8.6 Conic Sections

8.6 Conic Sections. 1. Types. 2. Standard Equation Forms. 3. Practice Problems. Types of Conic Sections. Parabolas. Types of Conic Sections. Circles. Types of Conic Sections. Elipses. Types of Conic Sections. Hyperbolas. Standard Equation Form. Standard Equation Form.

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8.6 Conic Sections

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  1. 8.6 Conic Sections 1 Types 2 Standard Equation Forms 3 Practice Problems

  2. Types of Conic Sections • Parabolas

  3. Types of Conic Sections • Circles

  4. Types of Conic Sections • Elipses

  5. Types of Conic Sections • Hyperbolas

  6. Standard Equation Form

  7. Standard Equation Form

  8. Standard Equation Form

  9. Identifying a Conic Section by Rewriting into Standard Form • Isolate the terms • Variables on the left of the equal sign • Constants on the right of the equal sign • Complete the square • Factor • Compare to the Standard Forms

  10. Identifying a Conic Section by Rewriting into Standard Form Example • Write the equation in standard form and identify the type of conic section it is.

  11. Identifying Conic Sections by Analyzing Coefficients • Put the equation into the form • Compare A and C using the following:

  12. Identifying Conic Sections by Analyzing Coefficients Examples State whether the following equation is a parabola, hyperbola, circle or ellipse. Since A and C have opposite signs, it is a hyperbola

  13. Identifying Conic Sections by Analyzing Coefficients Examples State whether the following equation is a parabola, hyperbola, circle or ellipse. Since A = C , it is a circle

  14. Identifying Conic Sections by Analyzing Coefficients Examples State whether the following equation is a parabola, hyperbola, circle or ellipse. Since A and C are both positive and not equal, it is a parabola

  15. Practice Problems • Page 450 Problems 4-9, 12-29, 33-38

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