Concept explainers
For Exercises 41–50, write the standard form of the equation of the hyperbola subject to the given conditions. (See Example 5)
Vertices:
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
COLLEGE ALGEBRA-ACCESS
- For Exercises 43–48, the equation represents a conic section (nondegenerative case). a. Identify the type of conic section. (See Example 6) b. Graph the equation on a graphing utility. 43. 4x – 4xy + 5y – 20 = 0 44. 6x + 4V3xy + 2y - 18x + 18V3y – 72 = 0 45. 2x – 6xy + 3y² - 4x + 12y – 9 = 0 46. 5x – 3xy + 2y – 6 = 0 47. 4x + 8xy + 4y – 2x – 5y – 2 = 0 48. 4x? + 8V3xy + 3y + 2x – 12y – 6 = 0arrow_forwardExercises 45–48 give equations for parabolas and tell how many units up or down and to the right or left each parabola is to be shifted. Find an equation for the new parabola, and find the new vertex, focus, and directrix.arrow_forwardExercises 27–34 give equations for hyperbolas. Put each equation instandard form and find the hyperbola’s asymptotes. Then sketch thehyperbola. Include the asymptotes and foci in your sketch.27. x2 - y2 = 1 28. 9x2 - 16y2 = 14429. y2 - x2 = 8 30. y2 - x2 = 431. 8x2 - 2y2 = 16 32. y2 - 3x2 = 333. 8y2 - 2x2 = 16 34. 64x2 - 36y2 = 2304arrow_forward
- For Exercises 13–22, a. Identify the center. b. Identify the vertices. c. Identify the foci. d. Write equations for the asymptotes. e. Graph the hyperbola. (See Examples 1-2) 13. 16 y? = 1 25 14. 25 y? = 1 36 y² 15. 4 = 1 36 y? 16. 9. = 1 49 17. 25y - 81x = 2025 18. 49y? 16x = 784 19. - 5x? + 7y² = -35 20. –7x + 1ly = -77 21. 25 16y 1 4x? 22. 81 16y? 1 49 225arrow_forwardIn Exercises 17–30, find the equations of the parabolas satisfying the given conditions. The vertex of each is at the origin.arrow_forwardExercises 45–48 give equations for parabolas and tell how many units up or down and to the right or left each parabola is to be shifted. Find an equation for the new parabola, and find the new vertex, focus, and directrix. 45. y2 = 4x, 46. x2 = 8y, right 1, down 7 47. x2 = 6y, left 2, down 3 48. y2 = -12x, right 4, up 3 left 3, down 2arrow_forward
- Find the equation y = ax2 + bx +c of the parabola that passes through the points (-2,0), (0, –14), (7,0) .arrow_forwardIn Exercises 37–40, find the center, foci, vertices, and eccentricity of the hyperbola, and sketch its graph using asymptotes as an aid.arrow_forwardIn Exercises 100–101, write the equation of each parabola in standard form. 100. Vertex: (-3, -4); The graph passes through the point (1, 4). 101. Vertex: (-3, -1); The graph passes through the point (-2, –3).arrow_forward
- In Exercises 5–16, determine the coordinates of the focus and the equation of the directrix of the given parabolas. Sketch each curve.arrow_forwardWhich are the foci for the hyperbola modeled by the equation (X-32 (x-1)²-1? 36 13 O (1. 10) and (1,-4) O (3.8) and (3, -8) O (1.9) and (1, -3) O (-6, 0) and (6, 0)arrow_forwardExercises 53–54 give equations for hyperbolas and tell how many units up or down and to the right or left each hyperbola is to be shifted. Find an equation for the new hyperbola, and find the new center, foci, vertices, and asymptotes. 53. y2/3-x2=1 right 1, up 3 54. y2-x2=1 left 1, down 1arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage