Concept explainers
For Exercises 27—34, an equation of a parabola
- Identify the vertex, value of p, focus, and focal diameter of the parabola.
- Identify the endpoints of the laths rectum.
- Graph the parabola.
- Write equations for the directrix and axis of symmetry. (See Examples 4)
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- 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_forwardIn Exercises 11–16, find the vertex, focus, and directrix of the parabola, and sketch its graph.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
- 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_forward2. Obtain the graph of the parabola y = -x² + 4x using transformations of the graph of y = x². Explain each step.arrow_forwardFind the equation y = ax2 + bx +c of the parabola that passes through the points (-2,0), (0, –14), (7,0) .arrow_forward
- 3. graph the parabola Y = 3(x - 2)2 + 1. plot five points on the parabola.arrow_forwardFind the equation of the parabola whose axis is parallel to the x-axis and passes through the points (3,1), (0,0), and (8,-4).arrow_forward1. A parabola has equation - 12x + y² – 24 = 0. Write the equation in standard form.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage