1. Sullivan Algebra and Trigonometry: Section 11.5 Objectives of this Section Identify a Conic Use a Rotation of Axes to Transform Equations Discuss an Equation Using Rotation of Axes Identify Conics Without a Rotation of Axes

2. Identifying Conics without Completing the Square Excluding degenerate cases, the equation (a) Defines a parabola if AC = 0. (b) Defines an ellipse (or a circle) if AC > 0. (c) Defines a hyperbola if AC < 0.

3. Identify the equation without completing the square. The equation is a hyperbola.

4. x y Consider rotating the x and y axis counterclockwise by an angle theta.

5. x y x y

7. Rotation Formulas

14. This is the equation of an ellipse with center at (0, 0) and major axis along the

15. x y

16. Identifying Conics without a Rotation of Axes Except for degenerate cases, the equation

17. This equation defines a hyperbola.