College Algebra
College Algebra
1st Edition
ISBN: 9780078035630
Author: Julie Miller
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Family of Curves
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XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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Chapter 7.1, Problem 6PE
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To calculate: The standard form of the given equation x2+y2−12x+14y+80=0 by completing the square.

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Consider the equation below. 16x² + y² + 16z² - 8y - 160z + 400 = 0 Reduce the equation to one of the standard forms.
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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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