1. Warm-Up 4/24 Parabola Circle Ellipse Hyperbola

3. Rigor: You will learn to identify and write equations of translated conic sections. Relevance: You will be able to solve real world problems using the equation of translated conic section.

4. 10-6 Translating Conic Sections

5. What is the standard-form equation of an ellipse with vertices (2, 3) and (22, 3), and one focus at (6, 3)? Sketch the ellipse. Center is the midpoint between the vertices. a = 12 – 2 = 10 c = 12 – 6 = 6 a is the distance from the center to a vertex. c is the distance from the center to a focus. Use c² = a² – b² to find b. 36 = 100 – b² – 64 = – b² 64 = b² Co-vertices (12, – 5) & (12, 11) ±8 = b a² = 100 c² = 36 Difference in x-coordinates: Horizontal

6. What are the center, vertices, foci, and asymptotes of the hyperbola with equation Sketch the hyperbola. Center (2, – 2) a² = 36 a = ± 6 vertices (– 4, – 2) & (8, – 2) Use c² = a² + b² to find c. c² = 36 + 64 c² = 100 c = ± 10 Foci (– 8, – 2) & (12, – 2) b² = 64 b = ± 8 box points (2, – 10) & (2, 6) x-term is positive: Horizontal

7. Assignment 10-6 WB p275, 1-13 EOO + 10 Due 4/29 Conics Project Due Dates: Section 2 + 1 due Today Sections 3 & 4 + 1 & 2 due April 30

10. What is the standard form of the equation below? Give all key points of the conic section. Ellipse Center (– 1, 3) a² = 36; a = ± 6 c² = a² – b² c² = 36 – 12 c² = 24 ; Vertices (5, 3) & (– 7, 3)

11. 7 th Warm-Up 4/24 Parabola Circle Ellipse Hyperbola

12. Conics Project Due Dates: Section 2 + 1 due Tomorrow April 25 Sections 3 & 4 + 1 & 2 due April 30

13. 10-6 Check PointsI will check your answers. Write equation in standard form. Assignment 10-6 WB p275, 1-13 EOO + 10

14. 10-6 Check Points Write equation in standard form. I will check your answers.

15. 10-6 Check Points

18. Analyze each equation. Complete each statement with the correct number.