Concepts Examples y2 - 4x - 10y + 21 = 0, or 1y - 522 = 41x + 12 x2 - 4x + y2 + 2y - 4 = 0, or 1x - 222 + 1y + 122 = 9 4x2 + y2 - 16 = 0, or x2 4 + y2 16 = 1 4x2 - y2 - 8x - 4y - 16 = 0, or 1x - 122 4 - 1y + 222 16 = 1 Parabola; vertex: 1-1, 52; opens to the right Circle; center: 12, -12; radius: 3 Ellipse; center: 10, 02; major axis: vertical Hyperbola; center: 11, -22; transverse axis: horizontal 10.4 Summary of the Conic Sections Conic sections in this chapter have equations that can be written in the following form. Ax2 +Cy2 +Dx +Ey +F =0 Chapter 10 Review Exercises Graph each parabola. In Exercises 1–4, give the domain, range, vertex, and axis of symmetry. In Exercises 5–8, give the domain, range, focus, directrix, and axis of symmetry. 1. x = 41y - 522 + 2 2. x = -1y + 122 - 7 3. x = 5y2 - 5y + 3 4. x = 2y2 - 4y + 1 5. y2 = - 2 3 x 6. y2 = 2x 7. 3x2 = y 8. x2 + 2y = 0 Write an equation for each parabola with vertex at the origin. 9. focus 14, 02 10. focus 10, -32 11. through the point 1-3, 42, opens up 12. through the point 12, 52, opens right Without actually graphing, identify the type of graph that each equation has. 13. y2 + 9x2 = 9 14. 9x2 - 16y2 = 144 15. 3y2 - 5x2 = 30 16. y2 + x = 4 17. 4x2 - y = 0 18. x2 + y2 = 25 19. 4x2 - 8x + 9y2 + 36y = -4 20. 9x2 - 18x - 4y2 - 16y - 43 = 0 1034 CHAPTER 10 Analytic Geometry Conic Section Characteristic Example Parabola Either A = 0 or C = 0, but not both. x2 - y - 4 = 0 y2 - x - 4y = 0 Circle A = C≠0 x2 + y2 - 16 = 0 Ellipse A≠C, AC70 25x2 + 16y2 - 400 = 0 Hyperbola AC60 x2 - y2 - 1 = 0 See the summary chart in this section.
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