Warm-Up

1. Warm-Up • Please review the equations written on the board. If you find that an equation represents a conic section, please make a note of the type it represents. • I will be calling on specific individuals in order to share your conclusions with the class.

2. Learning Objectives • Solve applied problems involving parabolas and ellipses

3. Conic Sections Formula Sheet • Please take time to look over the conic sections formula sheet I have handed out. • Using your notes and textbook, please attempt to fill in the appropriate formulas for the parabola and ellipse. • We will fill out the hyperbola section tomorrow

4. Real World Applications • Please take time to complete the word problem worksheet that has been handed out • Feel free to work in pairs/groups. Make sure to show your work. • Please ask questions if you are having difficulty • Draw a picture! It usually helps…

5. Learning Objectives • Solve applied problems involving parabolas and ellipses

6. Conic Sections – The Hyperbola

7. Warm-Up • What are the similarities/differences? • Compare the two graphs of the above equations using a Venn Diagram format

8. Comparison A hyperbola is the set of all points P(x, y)  in the plane such that| PF1 - PF2 | = 2a If F1(c, 0) and F2(-c, 0) are two fixed points in the plane and a is a constant, 0< c < a, then the set of all points P in the plane such thatPF1 + PF2 = 2ais an ellipse.  F1 and F2 are the foci of the ellipse.

9. Learning Objectives • Analyze hyperbolas with center at the origin • Find the asymptotes of a hyperbola • Analyze hyperbolas with center at (h,k)

12. Transverse Axis vs. Conjugate Axis

13. Let’s Try • State the coordinates of the vertices, the coordinates of the foci, the transverse and conjugate axis, and the equations of the asymptotes of the hyperbola defined by the equation

14. Let’s Try • State the coordinates of the vertices, the coordinates of the foci, the transverse and conjugate axis, and the equations of the asymptotes of the hyperbola defined by the equation

15. Station Activity • In groups, you will participate in an activity covering one of 5 topics. • You will have 10 minutes to work on each station • Please notify me if your group finishes early so that I can give you the next task.

16. Learning Objectives • Analyze hyperbolas with center at the origin • Find the asymptotes of a hyperbola • Analyze hyperbolas with center at (h,k)

17. Wrap Up Activities • Frayer Model Write-Up • What was the Muddiest Point?

18. Learning Objectives • Identify a conic • Identify conics without a rotation of axes

19. Warm-Up • Listed below is the standard form of the circle, ellipse, and hyperbola. Based on this information, how do you think we find the “general” form of a conic section?

20. General Form

21. General Form • B = 0 • A and C are not both zero • If AC = 0 we have a parabola • If AC > 0 we have an ellipse (or circle) • If AC < 0 we have a hyperbola

22. General Form • A and C are not both zero • If , we have a parabola • If , we have an ellipse (or circle) • If , we have a hyperbola

23. General Form to Standard Form

24. You try…

25. Learning Objectives • Identify a conic • Identify conics without a rotation of axes

26. Exit ticket • What would the general form of the equation describing the graph below be?