College Algebra
College Algebra
1st Edition
ISBN: 9780078035630
Author: Julie Miller
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 7.3, Problem 30PE

(a)

To determine

To calculate: The value of p for the equation of parabola −3x=y2.

(b)

To determine

To calculate: The focus of the parabola for the equation −3x=y2.

(c)

To determine

To calculate: The equation for the directrix of the parabola for the equation −3x=y2.

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For 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 %3D
For 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 -6
In Exercises 17-30, find the standard form of the equation of each parabola satisfying the given conditions. 17. Focus: (7,0); Directrix: x = -7 18. Focus: (9,0); Directrix: x = -9 19. Focus: (-5,0); Directrix: x = 5 20. Focus: (-10, 0); Directrix: x = 10 21. Focus: (0, 15); Directrix: y = -15 22. Focus: (0,20); Directrix: y = -20 23. Focus: (0, –25); Directrix: y = 25 24. Focus: (0, -15); Directrix: y = 15 25. Vertex: (2, -3); Focus: (2, -5) 26. Vertex: (5, -2); Focus: (7, -2) 27. Focus: (3, 2); Directrix: x = -1 28. Focus: (2, 4); Directrix: x = -4 29. Focus: (-3, 4); Directrix: y = 2 30. Focus: (7, –1); Directrix: y = -9

Chapter 7 Solutions

College Algebra

Ch. 7.1 - Skill Practice 1. Graph the ellipse, and identify...Ch. 7.1 - Prob. 2SPCh. 7.1 - Prob. 3SPCh. 7.1 - Prob. 4SPCh. 7.1 - Prob. 5SPCh. 7.1 - Prob. 6SPCh. 7.1 - Prob. 1PECh. 7.1 - Prob. 2PECh. 7.1 - Prob. 3PECh. 7.1 - Prob. 4PE
Ch. 7.1 - Prob. 5PECh. 7.1 - Prob. 6PECh. 7.1 - 1. The circle, the ellipse, the hyperbola, and the...Ch. 7.1 - Prob. 8PECh. 7.1 - Prob. 9PECh. 7.1 - Prob. 10PECh. 7.1 - Prob. 11PECh. 7.1 - Prob. 12PECh. 7.1 - Prob. 13PECh. 7.1 - Prob. 14PECh. 7.1 - Given x2a2+y2b2=1,whereab0, the ordered pairs...Ch. 7.1 - Prob. 16PECh. 7.1 - Prob. 17PECh. 7.1 - Prob. 18PECh. 7.1 - Prob. 19PECh. 7.1 - Prob. 20PECh. 7.1 - For Exercises 1112, from the equation of the...Ch. 7.1 - Prob. 22PECh. 7.1 - For Exercises 1322, a. Identify the center of the...Ch. 7.1 - Prob. 24PECh. 7.1 - For Exercises 13–22, a. Identify the center of...Ch. 7.1 - Prob. 26PECh. 7.1 - For Exercises 1322, a. Identify the center of the...Ch. 7.1 - For Exercises 1322, a. Identify the center of the...Ch. 7.1 - For Exercises 1322, a. Identify the center of the...Ch. 7.1 - For Exercises 13–22, a. Identify the center of...Ch. 7.1 - For Exercises 1322, a. Identify the center of the...Ch. 7.1 - For Exercises 13–22, a. Identify the center of...Ch. 7.1 - For Exercises 2332, a. Identify the center of the...Ch. 7.1 - Prob. 34PECh. 7.1 - For Exercises 2332, a. Identify the center of the...Ch. 7.1 - Prob. 36PECh. 7.1 - For Exercises 2332, a. Identify the center of the...Ch. 7.1 - Prob. 38PECh. 7.1 - For Exercises 2332, a. Identify the center of the...Ch. 7.1 - Prob. 40PECh. 7.1 - For Exercises 23–32, a. Identify the center of...Ch. 7.1 - Prob. 42PECh. 7.1 - For Exercises 33–42, a. Write the equation of the...Ch. 7.1 - For Exercises 33–42, a. Write the equation of the...Ch. 7.1 - For Exercises 3342, a. Write the equation of the...Ch. 7.1 - Prob. 46PECh. 7.1 - For Exercises 33–42, a. Write the equation of the...Ch. 7.1 - Prob. 48PECh. 7.1 - For Exercises 3342, a. Write the equation of the...Ch. 7.1 - Prob. 50PECh. 7.1 - For Exercises 43–56, write the standard form of an...Ch. 7.1 - For Exercises 43–56, write the standard form of an...Ch. 7.1 - For Exercises 4356, write the standard form of an...Ch. 7.1 - Prob. 54PECh. 7.1 - For Exercises 4356, write the standard form of an...Ch. 7.1 - For Exercises 4356, write the standard form of an...Ch. 7.1 - For Exercises 4356, write the standard form of an...Ch. 7.1 - Prob. 58PECh. 7.1 - For Exercises 4356, write the standard form of an...Ch. 7.1 - Prob. 60PECh. 7.1 - For Exercises 43–56, write the standard form of an...Ch. 7.1 - For Exercises 4356, write the standard form of an...Ch. 7.1 - For Exercises 4356, write the standard form of an...Ch. 7.1 - Prob. 64PECh. 7.1 - Prob. 87PECh. 7.1 - 58. The reflective property of an ellipse is the...Ch. 7.1 - Prob. 85PECh. 7.1 - A window above a door is to be made in the shape...Ch. 7.1 - Prob. 65PECh. 7.1 - Prob. 66PECh. 7.1 - Prob. 67PECh. 7.1 - Prob. 68PECh. 7.1 - Prob. 69PECh. 7.1 - Prob. 70PECh. 7.1 - Prob. 71PECh. 7.1 - Prob. 72PECh. 7.1 - Prob. 73PECh. 7.1 - Prob. 74PECh. 7.1 - Prob. 75PECh. 7.1 - Prob. 76PECh. 7.1 - Prob. 77PECh. 7.1 - 74. Halley’s Comet and the comet Hale-Bopp both...Ch. 7.1 - Prob. 79PECh. 7.1 - The planet Saturn orbits the Sun in an elliptical...Ch. 7.1 - For Exercises 7982, write the standard form of an...Ch. 7.1 - Prob. 82PECh. 7.1 - Prob. 83PECh. 7.1 - Prob. 84PECh. 7.1 - Prob. 89PECh. 7.1 - Prob. 90PECh. 7.1 - Prob. 91PECh. 7.1 - Prob. 92PECh. 7.1 - Prob. 93PECh. 7.1 - Prob. 94PECh. 7.1 - Prob. 95PECh. 7.1 - Prob. 96PECh. 7.1 - Prob. 97PECh. 7.1 - Prob. 98PECh. 7.1 - 95. An elliptical pool table is in the shape of an...Ch. 7.1 - Prob. 100PECh. 7.1 - Explain the difference between the graphs of the...Ch. 7.1 - Prob. 102PECh. 7.1 - Prob. 103PECh. 7.1 - Prob. 104PECh. 7.1 - Prob. 105PECh. 7.1 - 100. Find the pints on the ellipse that are twice...Ch. 7.1 - Prob. 107PECh. 7.1 - Prob. 108PECh. 7.1 - Prob. 109PECh. 7.1 - Prob. 110PECh. 7.1 - Prob. 111PECh. 7.2 - Skill Practice Repeat Example 1 with the equation:...Ch. 7.2 - Prob. 2SPCh. 7.2 - Prob. 3SPCh. 7.2 - Prob. 4SPCh. 7.2 - Prob. 5SPCh. 7.2 - Prob. 6SPCh. 7.2 - Prob. 7SPCh. 7.2 - Prob. 1PECh. 7.2 - Prob. 2PECh. 7.2 - Prob. 3PECh. 7.2 - Prob. 4PECh. 7.2 - Prob. 5PECh. 7.2 - Prob. 6PECh. 7.2 - Prob. 7PECh. 7.2 - Prob. 8PECh. 7.2 - Prob. 9PECh. 7.2 - Prob. 10PECh. 7.2 - Prob. 13PECh. 7.2 - Prob. 11PECh. 7.2 - Prob. 12PECh. 7.2 - Prob. 14PECh. 7.2 - Prob. 15PECh. 7.2 - Prob. 16PECh. 7.2 - Prob. 17PECh. 7.2 - For Exercises 7–8, a. Use the distance formula to...Ch. 7.2 - For Exercises 9–12, determine whether the...Ch. 7.2 - Prob. 20PECh. 7.2 - For Exercises 912, determine whether the...Ch. 7.2 - Prob. 22PECh. 7.2 - For Exercises 13–22, a. Identify the center....Ch. 7.2 - Prob. 24PECh. 7.2 - For Exercises 13–22, a. Identify the center....Ch. 7.2 - Prob. 26PECh. 7.2 - For Exercises 1322, a. Identify the center. b....Ch. 7.2 - Prob. 28PECh. 7.2 - For Exercises 13–22, a. Identify the center....Ch. 7.2 - Prob. 30PECh. 7.2 - For Exercises 13–22, a. Identify the center....Ch. 7.2 - Prob. 32PECh. 7.2 - For Exercises 2332, a. Identify the center. b....Ch. 7.2 - Prob. 34PECh. 7.2 - For Exercises 2332, a. Identify the center. b....Ch. 7.2 - Prob. 36PECh. 7.2 - For Exercises 23–32, a. Identify the center....Ch. 7.2 - Prob. 38PECh. 7.2 - For Exercises 2332, a. Identify the center. b....Ch. 7.2 - Prob. 40PECh. 7.2 - For Exercises 23–32, a. Identify the center....Ch. 7.2 - Prob. 42PECh. 7.2 - For Exercises 3340, a. Write the equation of the...Ch. 7.2 - Prob. 44PECh. 7.2 - For Exercises 3340, a. Write the equation of the...Ch. 7.2 - For Exercises 33–40, a. Write the equation of...Ch. 7.2 - For Exercises 33–40, a. Write the equation of...Ch. 7.2 - Prob. 48PECh. 7.2 - For Exercises 33–40, a. Write the equation of...Ch. 7.2 - Prob. 50PECh. 7.2 - For Exercises 41–50, write the standard form of...Ch. 7.2 - Prob. 52PECh. 7.2 - For Exercises 4150, write the standard form of the...Ch. 7.2 - Prob. 54PECh. 7.2 - For Exercises 4150, write the standard form of the...Ch. 7.2 - Prob. 56PECh. 7.2 - For Exercises 41–50, write the standard form of...Ch. 7.2 - For Exercises 4150, write the standard form of the...Ch. 7.2 - For Exercises 41–50, write the standard form of...Ch. 7.2 - For Exercises 41–50, write the standard form of...Ch. 7.2 - Prob. 61PECh. 7.2 - Prob. 62PECh. 7.2 - Prob. 63PECh. 7.2 - Prob. 64PECh. 7.2 - Prob. 65PECh. 7.2 - Determine the eccentricity of a hyperbola with a...Ch. 7.2 - Prob. 67PECh. 7.2 - Prob. 68PECh. 7.2 - Two radio transmitters are 1000 mi apart at points...Ch. 7.2 - Prob. 70PECh. 7.2 - 65. In September 2009, Australian astronomer...Ch. 7.2 - 66. The cross section of a cooling tower of a...Ch. 7.2 - Prob. 73PECh. 7.2 - Prob. 74PECh. 7.2 - Prob. 75PECh. 7.2 - Prob. 76PECh. 7.2 - Prob. 77PECh. 7.2 - Prob. 78PECh. 7.2 - Prob. 79PECh. 7.2 - Prob. 80PECh. 7.2 - Prob. 81PECh. 7.2 - Prob. 82PECh. 7.2 - Prob. 83PECh. 7.2 - Prob. 84PECh. 7.2 - Prob. 85PECh. 7.2 - Prob. 86PECh. 7.2 - Prob. 87PECh. 7.2 - Prob. 88PECh. 7.2 - Prob. 89PECh. 7.2 - Prob. 90PECh. 7.2 - Prob. 91PECh. 7.2 - Prob. 92PECh. 7.3 - Skill Practice Given a parabola defined by x2=4y,...Ch. 7.3 - Prob. 2SPCh. 7.3 - Prob. 3SPCh. 7.3 - Prob. 4SPCh. 7.3 - Prob. 5SPCh. 7.3 - Skill Practice Determine the standard form of an...Ch. 7.3 - Prob. 1PECh. 7.3 - For Exercises 1-6, identify each equation as...Ch. 7.3 - Prob. 3PECh. 7.3 - Prob. 4PECh. 7.3 - Prob. 5PECh. 7.3 - Prob. 6PECh. 7.3 - Prob. 7PECh. 7.3 - Prob. 8PECh. 7.3 - Prob. 9PECh. 7.3 - Prob. 10PECh. 7.3 - Prob. 11PECh. 7.3 - Prob. 12PECh. 7.3 - Prob. 13PECh. 7.3 - Prob. 14PECh. 7.3 - Prob. 15PECh. 7.3 - Prob. 16PECh. 7.3 - Prob. 17PECh. 7.3 - Prob. 18PECh. 7.3 - Prob. 19PECh. 7.3 - Prob. 20PECh. 7.3 - Prob. 21PECh. 7.3 - Prob. 22PECh. 7.3 - For Exercises 15–22, a model of the form is...Ch. 7.3 - Prob. 24PECh. 7.3 - For Exercises 1522, a model of the form...Ch. 7.3 - For Exercises 15–22, a model of the form is...Ch. 7.3 - For Exercises 15–22, a model of the form is...Ch. 7.3 - Prob. 28PECh. 7.3 - For Exercises 1522, a model of the form...Ch. 7.3 - Prob. 30PECh. 7.3 - A 20-in. satellite dish for a television has...Ch. 7.3 - Prob. 32PECh. 7.3 - For Exercises 2734, an equation of a parabola...Ch. 7.3 - Prob. 34PECh. 7.3 - For Exercises 2734, an equation of a parabola...Ch. 7.3 - Prob. 36PECh. 7.3 - For Exercises 2734, an equation of a parabola...Ch. 7.3 - Prob. 38PECh. 7.3 - For Exercises 2734, an equation of a parabola...Ch. 7.3 - Prob. 40PECh. 7.3 - For Exercises 35–44, an equation of a parabola or...Ch. 7.3 - Prob. 42PECh. 7.3 - For Exercises 35–44, an equation of a parabola or...Ch. 7.3 - Prob. 44PECh. 7.3 - For Exercises 35–44, an equation of a parabola or...Ch. 7.3 - Prob. 46PECh. 7.3 - For Exercises 3544, an equation of a parabola...Ch. 7.3 - Prob. 48PECh. 7.3 - For Exercises 3544, an equation of a parabola...Ch. 7.3 - Prob. 50PECh. 7.3 - For Exercises 45–52, an equation of a parabola is...Ch. 7.3 - For Exercises 4552, an equation of a parabola is...Ch. 7.3 - For Exercises 45–52, an equation of a parabola is...Ch. 7.3 - For Exercises 45–52, an equation of a parabola is...Ch. 7.3 - For Exercises 45–52, an equation of a parabola is...Ch. 7.3 - For Exercises 45–52, an equation of a parabola is...Ch. 7.3 - For Exercises 45–52, an equation of a parabola is...Ch. 7.3 - Prob. 58PECh. 7.3 - For Exercises 53–58, fill in the blanks, Let ...Ch. 7.3 - Prob. 60PECh. 7.3 - For Exercises 5358, fill in the blanks, Let |p|...Ch. 7.3 - Prob. 62PECh. 7.3 - For Exercises 53–58, fill in the blanks, Let ...Ch. 7.3 - Prob. 64PECh. 7.3 - 59. If the focal length of a parabola is 6 units...Ch. 7.3 - If the axis of symmetry of a parabola is given by...Ch. 7.3 - For Exercises 6168, determine the standard form of...Ch. 7.3 - Prob. 68PECh. 7.3 - For Exercises 6168, determine the standard form of...Ch. 7.3 - Prob. 70PECh. 7.3 - For Exercises 6168, determine the standard form of...Ch. 7.3 - Prob. 72PECh. 7.3 - For Exercises 6168, determine the standard form of...Ch. 7.3 - Prob. 74PECh. 7.3 - The Hubble Space Telescope was launched into space...Ch. 7.3 - 72. The James Webb Space Telescope (JWST) is a now...Ch. 7.3 - Prob. 77PECh. 7.3 - Prob. 78PECh. 7.3 - Prob. 79PECh. 7.3 - Prob. 80PECh. 7.3 - Prob. 81PECh. 7.3 - Prob. 82PECh. 7.3 - Prob. 83PECh. 7.3 - Prob. 84PECh. 7.3 - Prob. 85PECh. 7.3 - Prob. 1PRECh. 7.3 - Prob. 2PRECh. 7.3 - Prob. 3PRECh. 7.3 - Prob. 4PRECh. 7.3 - Prob. 5PRECh. 7.3 - Prob. 6PRECh. 7.3 - Prob. 7PRECh. 7.3 - Prob. 8PRECh. 7.3 - For Exercises 916, determine whether the equation...Ch. 7.3 - Prob. 10PRECh. 7.3 - Prob. 11PRECh. 7.3 - Prob. 12PRECh. 7.3 - Prob. 13PRECh. 7.3 - Prob. 14PRECh. 7.3 - Prob. 15PRECh. 7.3 - Prob. 16PRECh. 7.3 - Prob. 17PRECh. 7.3 - Prob. 18PRECh. 7.3 - Prob. 19PRECh. 7.3 - For Exercises 17–22, an equation of a degenerate...Ch. 7.3 - Prob. 21PRECh. 7.3 - Prob. 22PRECh. 7 - 1. How are the graphs of these ellipses similar...Ch. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - For Exercises 67, a. Write the equation of the...Ch. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - For Exercises 1720, an equation of a hyperbola is...Ch. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - For Exercises 3033, an equation of a parabola is...Ch. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 35RECh. 7 - Prob. 36RECh. 7 - Prob. 37RECh. 7 - Prob. 38RECh. 7 - Prob. 39RECh. 7 - Prob. 40RECh. 7 - Prob. 41RECh. 7 - Prob. 42RECh. 7 - Prob. 1TCh. 7 - Prob. 2TCh. 7 - Prob. 3TCh. 7 - Prob. 4TCh. 7 - Prob. 5TCh. 7 - Prob. 6TCh. 7 - Prob. 7TCh. 7 - Prob. 8TCh. 7 - Prob. 9TCh. 7 - For Exercises 916, a. Identify the equation as...Ch. 7 - Prob. 11TCh. 7 - Prob. 12TCh. 7 - For Exercises 916, a. Identify the equation as...Ch. 7 - Prob. 14TCh. 7 - Prob. 15TCh. 7 - For Exercises 916, a. Identify the equation as...Ch. 7 - 17. The entrance to a tunnel is in the shape of a...Ch. 7 - 18. Neptune orbits the Sun in an elliptical path...Ch. 7 - Prob. 19TCh. 7 - The middle span of the Golden Gate Bridge in San...Ch. 7 - Prob. 21TCh. 7 - Prob. 22TCh. 7 - Prob. 23TCh. 7 - Write the standard form of an equation of a...Ch. 7 - Prob. 25TCh. 7 - Prob. 26TCh. 7 - Prob. 27TCh. 7 - Prob. 28TCh. 7 - Prob. 29TCh. 7 - Prob. 30TCh. 7 - 1. Use long division to divide. Ch. 7 - Prob. 2CRECh. 7 - Prob. 3CRECh. 7 - Prob. 4CRECh. 7 - Prob. 5CRECh. 7 - Prob. 6CRECh. 7 - Prob. 7CRECh. 7 - Prob. 8CRECh. 7 - Prob. 9CRECh. 7 - Prob. 10CRECh. 7 - Prob. 11CRECh. 7 - Prob. 12CRECh. 7 - Prob. 13CRECh. 7 - Prob. 14CRECh. 7 - Prob. 15CRECh. 7 - Prob. 16CRECh. 7 - Prob. 17CRECh. 7 - Prob. 18CRECh. 7 - Prob. 19CRECh. 7 - Prob. 20CRECh. 7 - Prob. 21CRECh. 7 - Prob. 22CRECh. 7 - Prob. 23CRECh. 7 - Prob. 24CRECh. 7 - Prob. 25CRECh. 7 - Prob. 26CRECh. 7 - Prob. 27CRECh. 7 - Prob. 28CRECh. 7 - Prob. 29CRECh. 7 - Prob. 30CRE
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