1. 10.5 Rotation of Conics

2. 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.

3. 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.

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

5. How to Find θ Rotation through Given the Conic

6. How to Find θ Rotation through Given the Conic

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

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

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

10. Solve for System of Equations

11. Solve for System of Equations

12. Solve for System of Equations

13. Solve for System of Equations

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

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

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

17. Finding the intersection of two conics Given

18. Finding the intersection of two conics Given

19. Finding the intersection of two conics Given

20. Finding the intersection of two conics Given

21. Finding the intersection of two conics Given

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

23. Page 740 – 741 # 5, 23, 35, 50, 55