For Exercises 43–56, write the standard form of an equation of an ellipse subject to the given conditions. (See Example 5)
Vertices:
Foci:
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College Algebra (Collegiate Math)
- In Exercises 3–16, find the coordinates of the vertices and foci of the given ellipses. Sketch each curve.arrow_forwardExercises 49–52 give equations for ellipses and tell how many units up or down and to the right or left each ellipse is to be shifted. Find an equation for the new ellipse, and find the new foci, vertices, and center.arrow_forwardFor 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_forward
- In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. 35. (x – 2) = 8(y – 1) 37. (x + 1) = -8(y + 1) 39. (y + 3) = 12(x + 1) 41. (y + 1) = -&r 36. (x + 2) = 4(y + 1) 38. (x + 2) = -8(y + 2) 40. (y + 4)2 = 12(x + 2) %3D %3D 42. (y - 1) = -&rarrow_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_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
- In Exercises 1–8, find the eccentricity of the ellipse. Then find and graph the ellipse’s foci and directrices.arrow_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
- 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_forwardFor Exercises 27–34, an equation of a parabola x = 4py or y = 4px is given. a. Identify the vertex, value of p, focus, and focal diameter of the parabola. b. Identify the endpoints of the latus rectum. c. Graph the parabola. d. Write equations for the directrix and axis of symmetry. (See Examples 2-3) 27. x -4y 28. x -20y 29. 10y = 80x 30. 3y = 12x 31. 4x 40y 32. 2x 14y 33. y = 34. y = -2x = -X %3Darrow_forwardFor Exercises 79–82, write the standard form of an equation of the ellipse subject to the following conditions. 79. Center: (0, 0); Eccentricity: ; Major axis vertical of length 34 units 80. Center: (0, 0); Eccentricity: ; Major axis vertical of length 82 units 81. Foci: (0, – 1) and (8, – 1); Eccentricity: 82. Foci: (0, – 1) and (-6, –1); Eccentricity:arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage