1021 10.3 Hyperbolas CONCEPT PREVIEWMatch each equation with the correct graph. 5. x2 25 + y2 9 = 1 6. x2 9 + y2 25 = 1 7. x2 9 - y2 25 = 1 8. x2 25 - y2 9 = 1 A. x y 5 3 –3 B. x y 5 3 0 –3 –5 C. x y 3 5 0 –5 –3 D. x 0 y –3 3 5 –5 Graph each hyperbola. Give the foci, equations of the asymptotes, domain, and range. See Examples 1–3. 9. x2 16 - y2 9 = 1 10. x2 25 - y2 144 = 1 11. y2 25 - x2 49 = 1 12. y2 64 - x2 4 = 1 13. x2 - y2 = 9 14. x2 - 4y2 = 64 15. 9x2 - 25y2 = 225 16. 4y2 - 16x2 = 64 17. 4y2 - 25x2 = 100 18. x2 - 4y2 = 16 19. 9x2 - 4y2 = 1 20. 25y2 - 9x2 = 1 21. 1y - 722 36 - 1x - 422 64 = 1 22. 1x + 622 144 - 1y + 422 81 = 1 23. 1x + 322 16 - 1y - 222 9 = 1 24. 1y + 522 4 - 1x - 122 16 = 1 25. 161x + 522 - 1y - 322 = 1 26. 41x + 922 - 251y + 622 = 100 Graph each equation. Give the domain and range. Identify any that are functions. 27. y 3 = B1 + x2 16 28. x 3 = -B1 + y2 25 29. 5x = -21 + 4y2 30. 3y = 24x2 - 16 Write the equation of each hyperbola in standard form. Give the center, and determine whether the transverse axis is horizontal or vertical. See Example 4. 31. 11x2 + 66x - 2y2 - 4y = -75 32. 7x2 + 42x - 5y2 + 10y = -23 33. 25y2 - 250y - 49x2 - 392x = 1384 34. 4y2 - 32y - 9x2 - 90x = 305 35. 7x2 - 9y2 - 112x - 36y + 349 = 0 36. 3x2 - 10y2 - 30x + 160y - 595 = 0 37. 81y2 - x2 + 486y - 8x + 632 = 0 38. y2 - 64x2 + 14y + 768x - 2319 = 0 Find the eccentricity e of each hyperbola. Round to the nearest tenth. See Example 5. 39. x2 8 - y2 8 = 1 40. x2 2 - y2 18 = 1 41. 16y2 - 8x2 = 16 42. 8y2 - 2x2 = 16
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