10.5 Rotation of Conics

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10.5 Rotation of Conics
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The Standard Equation for all Conics

• Ax2 Bxy Cy2 Dx Ey F o
• So far B has equal zero and all graphs have been
  horizontal or vertical.
• Not anymore.

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The Standard Equation for all Conics

• Ax2 Bxy Cy2 Dx Ey F 0
• So far B has equal zero and all graphs have been
  horizontal or vertical.
• Not anymore.

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How to Find ?

• Rotation off the x axis
• Given the Conic

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How to Find ?

• Rotation through
• Given the Conic

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How to Find ?

• Rotation through
• Given the Conic

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When the graph of the conics is moved x and y are
called x and y'

• Ellipse rotated 45

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Write x and y in the new graph

• Let ? 30

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Find the coordinates of a point in a rotated
coordinate system

• Given ? 60 (3, 1) Find

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Solve for

• System of Equations

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Solve for

• System of Equations

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Solve for

• System of Equations

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Solve for

• System of Equations

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Classification of Conics by the Discriminant

• Ax2 Bxy Cy2 Dx Ey F 0

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Classification of Conics by the Discriminant

• Ax2 Bxy Cy2 Dx Ey F 0

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Classification of Conics by the Discriminant

• Ax2 Bxy Cy2 Dx Ey F 0

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Finding the intersection of two conics

• Given

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Finding the intersection of two conics

• Given

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Finding the intersection of two conics

• Given

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Finding the intersection of two conics

• Given

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Finding the intersection of two conics

• Given

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Homework

• Page 740 741
• 3, 19, 29, 47, 52

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• Page 740 741
• 5, 23, 35, 50, 55