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For Exercises 41–50, write the standard form of the equation of the hyperbola subject to the given conditions. (See Example 5)
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College Algebra (Collegiate Math)
- In Exercises 3–10, describe the curve represented by each equation. Identify the type of curve and its center (or vertex if it is a parabola). Sketch each curve.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.arrow_forwardFor 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_forward
- Exercises 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_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
- Exercises 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. x2/4-y2/5=1 right 2, up 2 54. x2/16-y2/9=1 left 2, down 1arrow_forwardIn Exercises 5–16, determine the coordinates of the focus and the equation of the directrix of the given parabolas. Sketch each curve.arrow_forwardFor Exercises 67–70, identify the equation as representing an ellipse or a hyperbola, and match the equation with the graph. (x – 5)² 67. (y + 2)² = 1 (x – 5)? 68. (y + 2)? = 1 49 36 36 49 (x - 5)? 69. (y + 2)² = 1 (y + 2)² = 1 (x - 5)? 49 36 70. 49 36 А. В. С. D. 15 12 41 6 -6-4-2 4 6 8 10 12 14 4 6 8 10 12 14 -6 -4 2. 4 6 8 10l 12 14 -6 1k 15 18 21 -6arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage