1. Concept Category #14 Conics in the Rectangular Coordinate System 6A I can derive the equations of circles, parabolas, ellipses and hyperbolas given the general equation in the second degree. I can find the key characteristics for each conic (i.e., focus, directrix, vertices, co-vertices, foci, asymptotes, minor axis, major axes). Foundational Skill: I can recognize and graph conic functions, including ellipses and hyperbolas.

2. Brainteaser: A radio tower services a 10 mile radius. You stop your car 5 miles east and 9 miles north of the tower. Will you be able to receive radio waves from the tower?

3. Task Find the equation of the circle centered at the origin(in terms of x and y) that passes through the point (7,24).

4. I. Classifying Conics & Analyzing Graphs A. Definition Conic Sections: The curves formed when a plane intersects the surface of a right cylindrical cone.

5. B. Visual

6. A. Definition Conics can be classified by computing the discriminant B 2 – 4AC, of equations of the form Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 B = 0 for the conics we will be working with

7. Example Identify each of the following conics:

8. Example Identify each of the following conics:

9. A. Definition Parabola is the set of all points in a plane whose distance from a fixed point is equal to its distance from a fixed line. Focus Directrix

10. B. Visual

11. Recall Parabolas? Standard form for the equation of a parabola: Vertex: (h, k) Axis of symmetry: x = h focus: (h, k + p) directrix: y = – p+k where p = 1/4a Vertex: (h, k) Axis of symmetry: y = k focus: (h + p, k) directrix: x = – p+h where p = 1/4a

12. C. Process Sketch the graph of y 2 + 2y + 8x + 17 = 0. Specify its vertex, focus, directrix and axis of symmetry. Determine the type of conic by using the discriminant

13. Standard form for the equation of a circle: center: (h,k) radius: r

14. What is the equation for the circle shown below? Example

15. Graph the following function.

16. Goal Problems: Determine choices for practice Recall & Reproduction Graph the following functions: 1. 2. 3. State the equation of a circle in general form which has a center at (5, -3) and a radius of 9. Routine Graph the following functions: 1. 2. 3. Write the center-radius equation of a circle that is tangent to the x-axis, with a center located at (4, -6).

17. Ellipses OR Standard Equation:

18. Center (h,k) a is the length of the semi-major axis (2a is the length of the major axis) b is the length of the semi-minor axis (2b is the length of the minor axis) c : For Both Types: vertices: (h + a, k) and (h – a, k) foci: (h + c, k) and (h – c, k) vertices: (h, k + a) and (h, k – a) foci: (h, k + c) and (h, k – c)

19. Hyperbolas: OR 0 a a vertices: (h – a, k) and (h + a, k) foci: (h – c, k) and (h + c, k) asymptotes: For Both: center: (h, k) vertices: (h, k – a) and (h, k + a) foci: (h, k – c) and (h, k + c) asymptotes:

20. Example: Graph the following function:

21. Example: Graph the following function:

22. Example: Graph the following function: 9x 2 -72x-16y 2 -32y-16=0

23. Determine the type of conic and justify your reasoning. Then sketch the graph

24. Goal Problems: Determine choices for practice Recall & Reproduction Routine Sketch the graph of - 4x 2 +9y 2 -48x-72y+144 = 0

25. Non-Routine 1. 2. Write an equation for the ellipse with vertices (4, 0) and (–2, 0) and foci (3, 0) and (–1, 0).

26. Hyperbolas: OR 0 a a vertices: (h – a, k) and (h + a, k) foci: (h – c, k) and (h + c, k) asymptotes: For Both: center: (h, k) vertices: (h, k – a) and (h, k + a) foci: (h, k – c) and (h, k + c) asymptotes:

27. Example: Graph the following function:

28. Example: Graph the following function:

29. Goal Problems: Determine choices for practice Recall & Reproduction Routine

30. Non-Routine

31. CCSSRecall & ReproductionRoutineNon-Routine G-GPE-3. G-GPE- 3.1 (CA) Read p160 - 165, §3.3 p165 #1-40 Read p167-172, §3.4 p172 #3-30, 33-42 Read p173-179 §3.5 p180 #9-28 Read p173-179 §3.5 p179 #1-4 G-GPE-3. G-GPE- 3.1 (CA) §11.1 p646 #1-8 §11.2 p659 #1-12 §11.1 p646 #9-28 §11.2 p659 #13-35 §11.2 p660 #36-40 Modeling: §11.1 p646 #29-32 §11.2 p660 #41, 42 Active Practice: