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8.1 Conic Sections (Parabolas)

8.1 Conic Sections (Parabolas). Parabolas with vertex (h, k). 8.1 Conic Sections (Ellipses). Ellipses with Center (h, k). 8.3 Conic Sections (Hyperbolas). Hyperbola with Center (h, k). Asymptotes. Examples. Find the vertex, focus, directrix, and focal width:. Vertex: (3, –2).

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8.1 Conic Sections (Parabolas)

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  1. 8.1 Conic Sections (Parabolas)

  2. Parabolas with vertex (h, k)

  3. 8.1 Conic Sections (Ellipses)

  4. Ellipses with Center (h, k)

  5. 8.3 Conic Sections (Hyperbolas)

  6. Hyperbola with Center (h, k) Asymptotes

  7. Examples Find the vertex, focus, directrix, and focal width: Vertex: (3, –2) Opens: left p: –4 Focus: (–1, –2) Directrix: x = 7 Focal width: 16

  8. Examples Find the vertices and foci: Center: (4, –2) a = √10 b = √6 c = √(10 – 6) = 2 Vertices: (4 + √10, –2) (4 + √10, –2) Foci: (6, –2) (2, –2)

  9. Examples Find the vertices and foci: Center: (4, –2) a = √6 b = √10 c = √(6 + 10) = 4 Vertices: (4 + √6, –2) (4 + √6, –2) Foci: (8, –2) (0, –2)

  10. Examples • Prove that the graph of • is an ellipse. • Find the center, vertices and foci. • Graph the ellipse by hand first. • Check the solution using your graphing calculator.

  11. (h + a, k) (h – c, k)  (h, k) (h – a, k) (h + c, k)

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