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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

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Chapter
Section
BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter 8.CT, Problem 21CT
Textbook Problem
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For Problems 18 25 graph each equation.

2 x 2 + 3 y 2 = 12

To determine

To graph:

The equation 2x2+3y2=12.

Explanation of Solution

Procedure used:

The standard equation of an ellipse is given below.

A(xh)2+B(yk)2=C

Here, A, B and C are nonzero real numbers of the same sign and (h,k) center points of the ellipse.

Substitute h for x in equation to find the endpoints of major axis.

Substitute k for y in equation to find the endpoints of minor axis.

Calculation:

Consider the given equation.

2x2+3y2=12...(1)

Compare the equation (1) with Ax2+By2=C. The value of A is 2 and B is 3.

Thus, the center points of the ellipse is (h,k)=(0,0).

Substitute 0 for x in equation (1).

2(0)2+3y2=120+3y2=12y2=123y=±2

The points on y-axis are (0,2),(0,2), where the ellipse cuts the y -axis.

Calculate the length of the intercepted portion on y axis as follows,

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Chapter 8 Solutions

Intermediate Algebra
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Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. 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Objective 1...Ch. 8.1 - Write a few paragraphs that summarize the ideas we...Ch. 8.1 - How would you convince someone that y=(x+3)2 is...Ch. 8.1 - How does the graph of y=x2 compare to the graph of...Ch. 8.1 - How does the graph of y=4x2 compare to the graph...Ch. 8.1 - Use a graphing calculator to check your graphs for...Ch. 8.1 - a. Graph y=x2, y=2x2, y=3x2, and y=4x2 on the same...Ch. 8.1 - a. Graph y=x2, y=(x2)2, y=(x3)2, and y=(x5)2 on...Ch. 8.1 - a. Graph y=x2, y=(x2)2+3, y=(x+4)22, and y=(x6)24...Ch. 8.1 - a Graph y=x212x+41 and y=x2+12x+41 on the same set...Ch. 8.2 - For Problems 110, answer true or false. Equations...Ch. 8.2 - For Problems 110, answer true or false. A circle...Ch. 8.2 - For Problems 110, answer true or false. A line...Ch. 8.2 - For Problems 110, answer true or false. The circle...Ch. 8.2 - For Problems 110, answer true or false. The circle...Ch. 8.2 - For Problems 110, answer true or false. The circle...Ch. 8.2 - For Problems 110, answer true or false. The graph...Ch. 8.2 - For Problems 110, answer true or false. The only x...Ch. 8.2 - For Problems 110, answer true or false. The origin...Ch. 8.2 - For Problems 110, answer true or false. The vertex...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 2334, find the centre and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the centre and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - Find the equation of the circle that passes...Ch. 8.2 - Find the equation of the circle that passes...Ch. 8.2 - Find the equation of the circle that passes...Ch. 8.2 - Find the equation of the circle that passes...Ch. 8.2 - What is the graph of x2+y2=4? Explain your answer.Ch. 8.2 - On which axis does the centre of the circle...Ch. 8.2 - Give a step-by-step description of how you would...Ch. 8.2 - Further Investigations The points (x,y) and (y,x)...Ch. 8.2 - Use a graphing calculator to check your graphs for...Ch. 8.2 - Use a graphing calculator to graph the circles in...Ch. 8.3 - For Problems 110, answer true or false. The length...Ch. 8.3 - For Problems 110, answer true or false. The major...Ch. 8.3 - For Problems 110, answer true or false. The axes...Ch. 8.3 - For Problems 110, answer true or false. The...Ch. 8.3 - For Problems 110, answer true or false. The x and...Ch. 8.3 - For Problems 110, answer true or false. The...Ch. 8.3 - For Problems 110, answer true or false. The...Ch. 8.3 - For Problems 110, answer true or false. The...Ch. 8.3 - For Problems 110, answer true or false. The center...Ch. 8.3 - For Problems 110, answer true or false. The center...Ch. 8.3 - For Problems 124, graph each ellipse. 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The graph...Ch. 8.4 - For Problems 110, answer true or false. Each...Ch. 8.4 - For Problems 110, answer true or false. To find...Ch. 8.4 - For Problem 110, answer true or false. The...Ch. 8.4 - For Problems 110, answer true or false. The...Ch. 8.4 - For Problem 110, answer true or false. The...Ch. 8.4 - For Problems 110, answer true or false. The center...Ch. 8.4 - For Problems 110, answer true or false. The...Ch. 8.4 - For Problem 110, answer true or false. The center...Ch. 8.4 - For Problems 16, find the intercepts and the...Ch. 8.4 - For Problems 16, find the intercepts and the...Ch. 8.4 - For Problems 16, find the intercepts and the...Ch. 8.4 - For Problems 16, find the intercepts and the...Ch. 8.4 - For Problems 16, find the intercepts and the...Ch. 8.4 - For Problems 16, find the intercepts and the...Ch. 8.4 - For Problems 718, graph each hyperbola. Objective...Ch. 8.4 - For Problems 718, graph each hyperbola. Objective...Ch. 8.4 - For Problems 718, graph each hyperbola. 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Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - The graph of equations of the form xy=k, where k...Ch. 8.4 - What is the graph of xy=0? Defend your answer.Ch. 8.4 - We have graphed various equations of the form...Ch. 8.4 - Explain the concept of an asymptote.Ch. 8.4 - Explain how asymptotes can be used to help graph...Ch. 8.4 - Are the graphs of x2y2=0 and y2x2=0 identical? Are...Ch. 8.4 - Graphing Calculator Activities To graph the...Ch. 8.4 - Graphing Calculator Activities For each of the...Ch. 8.S - Graph y=(x1)23.Ch. 8.S - Graph y=x26x11.Ch. 8.S - Write the equation of a circle that has its center...Ch. 8.S - Graph x24x+y2+6y+4=0.Ch. 8.S - Graph x2+25y2=25.Ch. 8.S - Graph 9x218x+y22y26=0.Ch. 8.S - Graph x24y2=4.Ch. 8.S - Graph 9x2+36x4y240y100=0.Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 912, write the equation of the circle...Ch. 8.CR - For Problems 912, write the equation of the circle...Ch. 8.CR - For Problems 912, write the equation of the circle...Ch. 8.CR - For Problems 912, write the equation of the circle...Ch. 8.CR - For Problems 1316, find the center and the length...Ch. 8.CR - For Problems 1316, find the center and the length...Ch. 8.CR - For Problems 1316, find the center and the length...Ch. 8.CR - For Problems 1316, find the center and the length...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 2530, find the equations of the...Ch. 8.CR - For Problems 2530, find the equations of the...Ch. 8.CR - For Problems 2530, find the equations of the...Ch. 8.CR - For Problems 2530, find the equations of the...Ch. 8.CR - For Problems 2530, find the equations of the...Ch. 8.CR - For Problems 2530, find the equations of the...Ch. 8.CR - For Problems 3150, graph each equation. 9x2+y2=81Ch. 8.CR - For Problems 3150, graph each equation. 9x2y2=81Ch. 8.CR - For Problems 3150, graph each equation. y=2x2+3Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation. y=2x24x3Ch. 8.CR - For Problems 3150, graph each equation. x2y2=9Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation. x2+y22y8=0Ch. 8.CR - For Problems 3150, graph each equation. y=(x+1)2+5Ch. 8.CR - For Problems 3150, graph each equation. y=12(x3)24Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation. x2+4y2=4Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CT - For Problems 14, find the vertex of each parabola....Ch. 8.CT - For Problems 14, find the vertex of each parabola....Ch. 8.CT - For Problems 14, find the vertex of each parabola....Ch. 8.CT - For Problems 14, find the vertex of each parabola....Ch. 8.CT - For Problems 57, write the equation of the circle...Ch. 8.CT - For Problems 57, write the equation of the circle...Ch. 8.CT - For Problems 57, write the equation of the circle...Ch. 8.CT - Find the length of minor axis of the ellipse...Ch. 8.CT - Find the length of major axis of the ellipse...Ch. 8.CT - Find the length of minor axis of the ellipse...Ch. 8.CT - For Problems 1517, find the equation of the...Ch. 8.CT - For Problems 1517, find the equation of the...Ch. 8.CT - For Problems 1517, find the equation of the...Ch. 8.CT - For Problems 1825, graph each equation. x24y2=16Ch. 8.CT - For Problem 1825 graph each equation. y=x2+4xCh. 8.CT - For Problems 1825, graph each equation....Ch. 8.CT - For Problems 1825 graph each equation. 2x2+3y2=12Ch. 8.CT - For Problem 1825 graph each equation. y=2x2+12x+22Ch. 8.CT - For Problems 1825, graph each equation. 9x2y2=9Ch. 8.CT - For Problems 1825, graph each equation....Ch. 8.CT - For Problems 1825, graph each equation....Ch. 8.CM - For Problems 14, evaluate each algebraic...Ch. 8.CM - For Problems 14, evaluate each algebraic...Ch. 8.CM - For Problems 14, evaluate each algebraic...Ch. 8.CM - For Problems 14, evaluate each algebraic...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 2530, factor each of the algebraic...Ch. 8.CM - For Problems 2530, factor each of the algebraic...Ch. 8.CM - For Problems 2530, factor each of the algebraic...Ch. 8.CM - For Problems 2530, factor each of the algebraic...Ch. 8.CM - For Problems 2530, factor each of the algebraic...Ch. 8.CM - For Problems 2530, factor each of the algebraic...Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 31-54, solve each of the equations....Ch. 8.CM - For Problems 31-54, solve each of the equations....Ch. 8.CM - For Problems 31-54, solve each of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 5564, solve inequality and express...Ch. 8.CM - For Problems 5564, solve inequality and express...Ch. 8.CM - For Problems 5564, solve inequality and express...Ch. 8.CM - For Problem 5564, solve inequality and express the...Ch. 8.CM - For Problems 5564, solve inequality and express...Ch. 8.CM - For Problems 5564, solve inequality and express...Ch. 8.CM - For Problems 5564, solve inequality and express...Ch. 8.CM - For Problem 5564, solve inequality and express the...Ch. 8.CM - For problem 55-64, solve each inequality and...Ch. 8.CM - For problem 55-64, solve each inequality and...Ch. 8.CM - For Problems 65-70, graph the following equations....Ch. 8.CM - For Problems 65-70, graph the following equations....Ch. 8.CM - For Problems 65-70, graph the following equations....Ch. 8.CM - For Problems 65-70, graph the following equations....Ch. 8.CM - For Problems 65-70, graph the following equations....Ch. 8.CM - For Problems 65-70, graph the following equations....Ch. 8.CM - For Problems 71 and 72, find the distance between...Ch. 8.CM - For Problems 71 and 72, find the distance between...Ch. 8.CM - For Problems 73-76, write the equation of a line...Ch. 8.CM - For Problems 73-76, write the equation of a line...Ch. 8.CM - For Problems 73-76, write the equation of a line...Ch. 8.CM - For Problem 73-76, write the equation of a line...Ch. 8.CM - Find the center and the length of a radius of the...Ch. 8.CM - Find the coordinates of the vertex of the...Ch. 8.CM - Find the equations of the asymptotes for the...Ch. 8.CM - Graph the ellipse 25x2+4y2=100Ch. 8.CM - Graph the hyperbola 9x24y2=36Ch. 8.CM - Graph the parabola y=2(x1)2+4Ch. 8.CM - For Problems 83-88, solve each problem by setting...Ch. 8.CM - For Problems 83-88, solve each problem by setting...Ch. 8.CM - For Problems 83-88, solve each problem by setting...Ch. 8.CM - For Problems 83-88, solve each problem by setting...Ch. 8.CM - For Problems 83-88, solve each problem by setting...Ch. 8.CM - For Problems 83-88, solve each problem by setting...

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