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Rotation of Axes; General Form of a Conic

Rotation of Axes; General Form of a Conic. Identifying Conics. Except for degenerate cases: Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 Defines a parabola if B 2 – 4AC = 0 Defines an ellipse (or a circle) if B 2 – 4AC < 0 Defines a hyperbola if B 2 – 4AC > 0.

leonard-acevedo
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Rotation of Axes; General Form of a Conic

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  1. Rotation of Axes; General Form of a Conic

  2. Identifying Conics Except for degenerate cases: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 • Defines a parabola if B2 – 4AC = 0 • Defines an ellipse (or a circle) if B2 – 4AC < 0 • Defines a hyperbola if B2 – 4AC > 0

  3. 1. Identify the graph of each equation without completing the square(Similar to p.417 #11-20, 43-52)

  4. 2. Identify the graph of each equation without completing the square(Similar to p.417 #11-20, 43-52)

  5. 3. Determine the appropriate rotation formulas to use so that the new equation contains no xy-term(Similar to p.417 #21-30)

  6. Rotation Formulas

  7. Standard Form of a Parabola

  8. Standard Form of a Ellipse (a>b)

  9. Standard Form of a Hyperbola

  10. 4. Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation(Similar to p.418 #31-42)

  11. 5. Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation(Similar to p.418 #31-42)

  12. 6. Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation(Similar to p.418 #31-42)

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