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Warm-Up 4/24

Warm-Up 4/24 . Parabola. Circle. Ellipse. Hyperbola. 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. 10-6 Translating Conic Sections.

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Warm-Up 4/24

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

  2. 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.

  3. 10-6 Translating Conic Sections

  4. 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. Difference in x-coordinates: Horizontal Center is the midpoint between the vertices. Center = a is the distance from the center to a vertex. a = 12 – 2 = 10 • a² = 100 c is the distance from the center to a focus. • • c² = 36 c = 12 – 6 = 6 Usec² = a²– b² to find b. 36=100– b² • • • • • – 64 = – b² 64 = b² ±8 = b • Co-vertices (12, – 5) & (12, 11)

  5. x-term is positive: Horizontal What are the center, vertices, foci, and asymptotes of the hyperbola with equation Sketch the hyperbola. Asymptotes Center (2, – 2) vertices (– 4, – 2) & (8, – 2) a² = 36 a = ± 6 Use c² =a²+ b²to find c. • c² =36+ 64 Foci (– 8, – 2) & (12, – 2) c² =100 c = ± 10 • • • • • box points (2, – 10) & (2, 6) b² = 64 b = ± 8 •

  6. 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

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

  8. 7th Warm-Up 4/24 State whether the graph is a circle, parabola, ellipse, or hyperbola. 1. 2. 3. 4. Hyperbola Ellipse Circle Parabola

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

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

  11. 10-6 Check Points • I will check your answers. Write equation in standard form.

  12. 10-6 Check Points

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

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