Algebra and Trigonometry - NASTA Edition - Package
Algebra and Trigonometry - NASTA Edition - Package
5th Edition
ISBN: 9780133131482
Author: Blitzer
Publisher: PEARSON
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Concept explainers

Vertices Of An Ellipse
In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…
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Textbook Question
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Chapter 10, Problem 1MCCP

In Exercises 1-5, graph each ellipse. Give the location of the foci.

x 2 25 + y 2 4 = 1

Expert Solution & Answer
Check Mark
To determine

To graph: The equation of the ellipse x225+y24=1 and determine its foci.

Explanation of Solution

Given:

The equation of the ellipse is x225+y24=1

Graph:

Compare the given equation with the standard form of an ellipse, x225+y24=1 and obtain:

a2=25a=5

and

b2=25b=2

Evaluate the foci at the coordinates given by (±ae,0), where e is calculated as:

e=1−b2a2=1−425=2125=215

Thus,

ae=5⋅(215)=21

Therefore, the foci lie at (±21,0).

Plot the graph using the above data as:

Algebra and Trigonometry - NASTA Edition - Package, Chapter 10, Problem 1MCCP

Interpretation:

The graph has its foci at (±21,0).

The transverse axis is along the x-axis.

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Chapter 10 Solutions

Algebra and Trigonometry - NASTA Edition - Package

Ch. 10.1 - Fill in each blank so that the resulting statement...Ch. 10.1 - Prob. 2CVCCh. 10.1 - Prob. 3CVCCh. 10.1 - Prob. 4CVCCh. 10.1 - The graph of (x+1)225+(y4)29=1 has its center...Ch. 10.1 - Prob. 6CVCCh. 10.1 - Prob. 7CVCCh. 10.1 - 8. In the equation , we complete the square on x...Ch. 10.1 - Prob. 1ECh. 10.1 - Prob. 2E
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An architect designs two houses dial arc...Ch. 10.2 - Prob. 64ECh. 10.2 - Prob. 65ECh. 10.2 - Prob. 66ECh. 10.2 - Prob. 67ECh. 10.2 - Prob. 68ECh. 10.2 - Prob. 69ECh. 10.2 - Prob. 70ECh. 10.2 - Prob. 71ECh. 10.2 - Prob. 72ECh. 10.2 - Prob. 73ECh. 10.2 - Prob. 74ECh. 10.2 - Prob. 75ECh. 10.2 - Prob. 76ECh. 10.2 - Prob. 77ECh. 10.2 - Prob. 78ECh. 10.2 - Prob. 79ECh. 10.2 - Prob. 80ECh. 10.2 - Make Sense? In Exercises 81-84, determine whether...Ch. 10.2 - Prob. 82ECh. 10.2 - Prob. 83ECh. 10.2 - Prob. 84ECh. 10.2 - Prob. 85ECh. 10.2 - Prob. 86ECh. 10.2 - Prob. 87ECh. 10.2 - Prob. 88ECh. 10.2 - Prob. 89ECh. 10.2 - Prob. 90ECh. 10.2 - Prob. 91ECh. 10.2 - Prob. 92ECh. 10.2 - Prob. 93ECh. 10.2 - Prob. 94ECh. 10.3 - The set of all points in a plane that are...Ch. 10.3 - Prob. 2CVCCh. 10.3 - Use the graph shown to answer Exercises 2-5. If...Ch. 10.3 - Prob. 4CVCCh. 10.3 - Use the graph shown to answer Exercises 2-5. 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Look at the satellite dish shown in Exercise...Ch. 10.3 - Prob. 75ECh. 10.3 - Prob. 76ECh. 10.3 - Prob. 77ECh. 10.3 - Prob. 78ECh. 10.3 - Prob. 79ECh. 10.3 - Prob. 80ECh. 10.3 - Prob. 81ECh. 10.3 - Prob. 82ECh. 10.3 - Prob. 83ECh. 10.3 - Prob. 84ECh. 10.3 - Prob. 85ECh. 10.3 - Prob. 86ECh. 10.3 - In Exercises 85-88, determine whether each...Ch. 10.3 - Prob. 88ECh. 10.3 - Prob. 89ECh. 10.3 - Prob. 90ECh. 10.3 - Prob. 91ECh. 10.3 - Prob. 92ECh. 10.3 - Prob. 93ECh. 10.3 - Prob. 94ECh. 10.4 - Prob. 1CVCCh. 10.4 - Prob. 2CVCCh. 10.4 - Prob. 3CVCCh. 10.4 - Prob. 9ECh. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 37ECh. 10.4 - Prob. 38ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Prob. 43ECh. 10.4 - Prob. 44ECh. 10.4 - Prob. 45ECh. 10.4 - Prob. 46ECh. 10.4 - Prob. 47ECh. 10.4 - Prob. 48ECh. 10.4 - Prob. 49ECh. 10.4 - Prob. 50ECh. 10.4 - Prob. 51ECh. 10.4 - Prob. 52ECh. 10.4 - Prob. 53ECh. 10.4 - Prob. 54ECh. 10.4 - Prob. 55ECh. 10.4 - Prob. 56ECh. 10.4 - Prob. 57ECh. 10.4 - Prob. 58ECh. 10.4 - Prob. 59ECh. 10.4 - Prob. 60ECh. 10.4 - Prob. 61ECh. 10.4 - Prob. 62ECh. 10.4 - Prob. 63ECh. 10.4 - Prob. 64ECh. 10.4 - Prob. 65ECh. 10.4 - Prob. 66ECh. 10.4 - Prob. 67ECh. 10.4 - Prob. 68ECh. 10.4 - Prob. 70ECh. 10.4 - Prob. 71ECh. 10.4 - Prob. 72ECh. 10.5 - Prob. 1CVCCh. 10.5 - Prob. 2CVCCh. 10.5 - Prob. 3CVCCh. 10.5 - Prob. 4CVCCh. 10.5 - Prob. 1ECh. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - Prob. 6ECh. 10.5 - Prob. 7ECh. 10.5 - Prob. 8ECh. 10.5 - Prob. 9ECh. 10.5 - Prob. 10ECh. 10.5 - Prob. 11ECh. 10.5 - Prob. 12ECh. 10.5 - Prob. 13ECh. 10.5 - Prob. 14ECh. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 - Prob. 21ECh. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 - Prob. 26ECh. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - Prob. 32ECh. 10.5 - Prob. 33ECh. 10.5 - Prob. 34ECh. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Prob. 37ECh. 10.5 - Prob. 38ECh. 10.5 - Prob. 39ECh. 10.5 - Prob. 40ECh. 10.5 - Prob. 41ECh. 10.5 - Prob. 42ECh. 10.5 - Prob. 43ECh. 10.5 - Prob. 44ECh. 10.5 - In Exercises 45-52, use your answers from...Ch. 10.5 - Prob. 46ECh. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.5 - Prob. 50ECh. 10.5 - Prob. 51ECh. 10.5 - Prob. 52ECh. 10.5 - Prob. 53ECh. 10.5 - Prob. 54ECh. 10.5 - Prob. 55ECh. 10.5 - Prob. 56ECh. 10.5 - Prob. 57ECh. 10.5 - Prob. 58ECh. 10.5 - Prob. 59ECh. 10.5 - Prob. 60ECh. 10.5 - Prob. 61ECh. 10.5 - Prob. 62ECh. 10.5 - Prob. 63ECh. 10.5 - Prob. 64ECh. 10.5 - Prob. 65ECh. 10.5 - Prob. 66ECh. 10.5 - Prob. 67ECh. 10.5 - Prob. 68ECh. 10.5 - Prob. 69ECh. 10.5 - Prob. 70ECh. 10.5 - Prob. 71ECh. 10.5 - Prob. 72ECh. 10.5 - Prob. 73ECh. 10.5 - Prob. 74ECh. 10.5 - Prob. 75ECh. 10.5 - Prob. 76ECh. 10.5 - Prob. 77ECh. 10.5 - Prob. 78ECh. 10.5 - Prob. 79ECh. 10.5 - Prob. 80ECh. 10.5 - Prob. 81ECh. 10.5 - Prob. 82ECh. 10.5 - Prob. 83ECh. 10.5 - Prob. 84ECh. 10.5 - Use the equations for the path of a projectile...Ch. 10.5 - Prob. 86ECh. 10.5 - Prob. 87ECh. 10.5 - Prob. 88ECh. 10.5 - Prob. 89ECh. 10.5 - Prob. 90ECh. 10.5 - Prob. 91ECh. 10.5 - Prob. 92ECh. 10.5 - Prob. 93ECh. 10.5 - Prob. 94ECh. 10.5 - Prob. 95ECh. 10.6 - Prob. 1CVCCh. 10.6 - Prob. 2CVCCh. 10.6 - Fill in each blank so that the resulting statement...Ch. 10.6 - Fill in each blank so that the resulting statement...Ch. 10.6 - Fill in each blank so that the resulting statement...Ch. 10.6 - Prob. 1ECh. 10.6 - Prob. 2ECh. 10.6 - Prob. 3ECh. 10.6 - Prob. 4ECh. 10.6 - Prob. 5ECh. 10.6 - Prob. 6ECh. 10.6 - Prob. 7ECh. 10.6 - Prob. 8ECh. 10.6 - Prob. 9ECh. 10.6 - Prob. 10ECh. 10.6 - Prob. 11ECh. 10.6 - Prob. 12ECh. 10.6 - Prob. 13ECh. 10.6 - Prob. 14ECh. 10.6 - Prob. 15ECh. 10.6 - Prob. 16ECh. 10.6 - Prob. 17ECh. 10.6 - Prob. 18ECh. 10.6 - Prob. 19ECh. 10.6 - Prob. 20ECh. 10.6 - Prob. 21ECh. 10.6 - Prob. 22ECh. 10.6 - Prob. 23ECh. 10.6 - Prob. 24ECh. 10.6 - Prob. 25ECh. 10.6 - Prob. 26ECh. 10.6 - Prob. 27ECh. 10.6 - Prob. 28ECh. 10.6 - Prob. 29ECh. 10.6 - Halley's Cornel has an elliptical orbit with the...Ch. 10.6 - Prob. 31ECh. 10.6 - Prob. 32ECh. 10.6 - 33. How are the conics described in terms of a...Ch. 10.6 - Prob. 34ECh. 10.6 - Prob. 35ECh. 10.6 - Prob. 36ECh. 10.6 - Prob. 37ECh. 10.6 - Prob. 38ECh. 10.6 - Prob. 39ECh. 10.6 - Prob. 40ECh. 10.6 - Prob. 41ECh. 10.6 - Prob. 42ECh. 10.6 - Prob. 43ECh. 10.6 - Prob. 44ECh. 10.6 - Prob. 45ECh. 10.6 - Prob. 46ECh. 10.6 - Prob. 47ECh. 10.6 - Prob. 48ECh. 10.6 - Prob. 49ECh. 10.6 - Prob. 50ECh. 10.6 - Prob. 51ECh. 10.6 - Prob. 52ECh. 10.6 - Prob. 53ECh. 10.6 - Prob. 54ECh. 10.6 - Prob. 55ECh. 10.6 - Prob. 56ECh. 10.6 - Prob. 57ECh. 10 - In Exercises 1-5, graph each ellipse. Give the...Ch. 10 - Prob. 2MCCPCh. 10 - Prob. 3MCCPCh. 10 - Prob. 4MCCPCh. 10 - Prob. 5MCCPCh. 10 - In Exercises 6-11, graph each hyperbola. Give the...Ch. 10 - In Exercises 6-11, graph each hyperbola. Give the...Ch. 10 - In Exercises 6-11, graph each hyperbola. Give the...Ch. 10 - In Exercises 6-11, graph each hyperbola. Give the...Ch. 10 - In Exercises 6-11. graph each hyperbola. Give the...Ch. 10 - In Exercises 6-11, graph each hyperbola. Give the...Ch. 10 - In Exercises 12-13 , graph each parabola. Give the...Ch. 10 - In Exercises 12-13 . graph each parabola. Give the...Ch. 10 - In Exercises 17-24, graph each equation. x2+y2=4Ch. 10 - In Exercises 17-24, graph each equation. 18. Ch. 10 - In Exercises 17-24, graph each equation. 19. Ch. 10 - In Exercises 17-24, graph each equation. 20. Ch. 10 - In Exercises 17-24, graph each equation. 21. Ch. 10 - In Exercises 17-24, graph each equation. 22. Ch. 10 - In Exercises 17-24, graph each equation....Ch. 10 - In Exercises 17-24, graph each equation....Ch. 10 - Prob. 22MCCPCh. 10 - In Exercises 25-30, find the standard form of the...Ch. 10 - Prob. 24MCCPCh. 10 - Prob. 25MCCPCh. 10 - In Exercises 25-30, find the standdpd form of the...Ch. 10 - In Exercises 25-30, find the standard form of the...Ch. 10 - A semielliptical archway over a one-way road has a...Ch. 10 - A lithotriper is used to disentegrate kidney...Ch. 10 - 33. An explosion is recorded by two forest...Ch. 10 - A domed ceiling is a parabolic surface. Ten meters...Ch. 10 - In Exercises 1-8, graph each ellipse and locate...Ch. 10 - Prob. 2RECh. 10 - In Exercises 1-8, graph each ellipse and locate...Ch. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Prob. 20RECh. 10 - In Exercises 15-22, graph each hyperbula. Locate...Ch. 10 - In Exercises 15-22, graph each hyperbola. Locate...Ch. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - 25. Explain why it is not possible for a hyperbola...Ch. 10 - 26. Radio tower M2 is located 200 miles due west...Ch. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Prob. 29RECh. 10 - Prob. 30RECh. 10 - In Exercises 27-33, find the vertex, focus, and...Ch. 10 - Prob. 32RECh. 10 - Prob. 33RECh. 10 - Prob. 34RECh. 10 - Prob. 35RECh. 10 - Prob. 36RECh. 10 - Prob. 37RECh. 10 - Prob. 38RECh. 10 - In Exercises 39 42, identify the conic represented...Ch. 10 - In Exercises 39-42, identify the conic represented...Ch. 10 - In Exercises 39-42, identify the conic represented...Ch. 10 - In Exercises 39-42. identify the conic represented...Ch. 10 - In Exercises 43 -46, identify the conic...Ch. 10 - In Exercises 43 -46, identify the conic...Ch. 10 - In Exercises 43 -46, identify the conic...Ch. 10 - In Exercises 43 -46 , identify the conic...Ch. 10 - Prob. 47RECh. 10 - Prob. 48RECh. 10 - Prob. 49RECh. 10 - Prob. 50RECh. 10 - Prob. 51RECh. 10 - In Exercises 52 -57. eliminate the parameter and...Ch. 10 - In Exercises 52 -57 . eliminate the parameter and...Ch. 10 - In Exercises 52 -57, eliminate the parameter and...Ch. 10 - In Exercises 52 -57. eliminate the parameter and...Ch. 10 - In Exercises 52 -57. eliminate the parameter and...Ch. 10 - In Exercises 52 -57. eliminate the parameter and...Ch. 10 - Find two different sets of parametric equations...Ch. 10 - 59. The path of a projectile that is launched h...Ch. 10 - Prob. 60RECh. 10 - Prob. 61RECh. 10 - Prob. 62RECh. 10 - Prob. 63RECh. 10 - Prob. 64RECh. 10 - Prob. 65RECh. 10 - In Exercises 1-5. graph the conic section with the...Ch. 10 - Prob. 2TCh. 10 - Prob. 3TCh. 10 - Prob. 4TCh. 10 - Prob. 5TCh. 10 - In Exercises 6-8, find the standard form of the...Ch. 10 - Prob. 7TCh. 10 - In Exercises 6-8, find the standard form of the...Ch. 10 - In Exercises 6 ft, find the standard form of the...Ch. 10 - 10. An engineer is designing headlight units for...Ch. 10 - In Exercises 11-12, identify each equation without...Ch. 10 - In Exercises 11-12, identify each equation without...Ch. 10 - Prob. 13TCh. 10 - In Exercises 14 -15. eliminate the parameter and...Ch. 10 - In Exercises 14-15 eliminate the parameter and...Ch. 10 - Prob. 16TCh. 10 - Prob. 17TCh. 10 - Solve each equation or inequality in Exercises...Ch. 10 - Solve each equation or inequality in Exercises...Ch. 10 - Solve each equation or inequality in Exercises...Ch. 10 - Solve each equation or inequality in Exercises...Ch. 10 - Solve each equation or inequality in Exercises...Ch. 10 - Solve each equation or inequality in Exercises...Ch. 10 - Solve each equation or inequality in Exercises...Ch. 10 - Solve each system in Exercises 8-10. 8. Ch. 10 - Solve each system in Exercises 8-10. 9. {...Ch. 10 - Solve each system in Exercises 8-10. (Use...Ch. 10 - In Exercises 11-13, graph each equation, function,...Ch. 10 - In Exercises 11-13, graph each equation, function,...Ch. 10 - In Exercises 11-13, graph each equation, function,...Ch. 10 - a. List all possible rational roots of...Ch. 10 - 15. The figure shows ihe graph of and its two...Ch. 10 - 16. If Ch. 10 - 17. Expand using logarithmic properties. Where...Ch. 10 - 18. Write the slope-intercept form of the equation...Ch. 10 - Rent-a-Truck charges a daily rental rate for a...Ch. 10 - The local cable television company offers two...Ch. 10 - 21. Verify the identity: Ch. 10 - Graph one complete cycle of y=2cos(2x+).Ch. 10 - Prob. 23CRECh. 10 - Solve for :sin2=sin,02.Ch. 10 - In oblique triangle ABC,A=64,B=72,anda=13.6. Solve...

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