10.5 Rotation of Conics. The Standard Equation for all Conics Ax 2 + Bxy + Cy 2 + Dx + Ey + F = o So far B has equal zero and all graphs have been horizontal.

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Presentation transcript:

10.5 Rotation of Conics

The Standard Equation for all Conics Ax 2 + Bxy + Cy 2 + Dx + Ey + F = o So far B has equal zero and all graphs have been horizontal or vertical. Not anymore.

The Standard Equation for all Conics Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 So far B has equal zero and all graphs have been horizontal or vertical. Not anymore.

How to Find θ Rotation off the x axis Given the Conic

How to Find θ Rotation through Given the Conic

How to Find θ Rotation through Given the Conic

When the graph of the conics is moved x and y are called x‘ and y' Ellipse rotated 45°

Write x and y in the new graph Let θ = 30°

Find the coordinates of a point in a rotated coordinate system Given θ = 60° ; (3, 1) Find

Solve for System of Equations

Solve for System of Equations

Solve for System of Equations

Solve for System of Equations

Classification of Conics by the Discriminant Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0

Classification of Conics by the Discriminant Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0

Classification of Conics by the Discriminant Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0

Finding the intersection of two conics Given

Finding the intersection of two conics Given

Finding the intersection of two conics Given

Finding the intersection of two conics Given

Finding the intersection of two conics Given

Homework Page 740 – 741 #3, 19, 29, 47, 52

Page 740 – 741 # 5, 23, 35, 50, 55