For Exercises 9–16,
a. Identify the equation as representing a
b. Graph the curve.
c. Identify key features of the graph. That is,
•If the equation represents a circle, identify the center and radius.
•If the equation represents an ellipse, identify the center, vertices, endpoints of the minor axis, foci, and eccentricity.
•If the equation represents a hyperbola, identify the center, vertices, foci, equations of the asymptotes, and eccentricity.
•If the equation represents a parabola, identify the vertex, focus, endpoints of the latus rectum, equation of the of the directrix, and equation of the axis of symmetry.
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
COLLEGE ALGEBRA CUSTOM -ALEKS ACCESS
- 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 3–16, find the coordinates of the vertices and foci of the given ellipses. Sketch each curve.arrow_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_forward
- Exercises 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_forwardIn Exercises 11–16, find the vertex, focus, and directrix of the parabola, and sketch its graph.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_forward
- In Exercises 1–8, find the eccentricity of the ellipse. Then find and graph the ellipse’s foci and directrices.arrow_forwardIn Problems 29–36, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equationarrow_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
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage