1. Warm Up

2. Some rules of thumb for classifying Suppose the equation is written in the form: Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0, where A – F are real coefficients and B = 0 If A = 0 OR C = 0 (but not both) then the conic is a parabola (because one variable is squared and the other isn’t) If A = C then it’s a circle If A and C have the same sign and are not equal, then its an ellipse (because the squared terms are being ADDED) If A and C have different signs then it is a hyperbola (because the squared terms are being SUBTRACTED)

3. Example 6-1a Write the equation is standard form. Write the equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation. Original equation Divide each side by 18. Isolate terms.

4. Write the equation in standard form. State whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. Then graph the equation. Example 6-1b Answer: circle

5. Example 6-2a Since A and C have opposite signs, the graph is a hyperbola. Without writing the equation in standard form, state whether the graph of is a parabola, circle, ellipse, or hyperbola. Answer: and

6. Example 6-2a Without writing the equation in standard form, state whether the graph of is a parabola, circle, ellipse, or hyperbola. Answer: and Since the graph is a circle.

7. Example 6-2a Without writing the equation in standard form, state whether the graph of is a parabola, circle, ellipse, or hyperbola. Answer: and Since this graph is a parabola.

8. Without writing the equation in standard form, state whether the graph of the equation is a parabola, circle, ellipse, or hyperbola. a. b. c. Example 6-2b Answer: hyperbola Answer: ellipse Answer: parabola