1. 10.4 Rotation and Systems of Quadratic Equations

2. Quick Review

3. Quick Review Solutions

4. What you’ll learn about  Second-Degree Equations in Two Variables  Translating Axes versus Translating Graphs  Rotation of Axes  Discriminant Test … and why You will see ellipses, hyperbolas, and parabolas as members of the family of conic sections rather than as separate types of curves.

5. Translation-of-Axes Formulas

6. Example Translation Formula

8. Rotation-of-Axes Formulas

9. Rotation of Cartesian Coordinate Axes

10. Example Rotation of Axes

12. Coefficients for a Conic in a Rotated System

13. Angle of Rotation to Eliminate the Cross-Product Term

14. Discriminant Test

15. Conics and the Equation Ax 2 +Bxy+Cy 2 +Dx+Ey+F=0