BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

Solutions

Chapter
Section
BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

CONCEPTS

An graph of the equation x 2 b 2 + y 2 a 2 = 1 with a > b > 0 is an ellipse with vertices ( ____, ____ ) and ( ____, ____ ) and foci ( 0 , ± c ) , where c = __________. So the graph of x 2 4 2 + y 2 5 2 = 1 is an ellipse with vertices ( ____, ____ ) and ( ____, ____ ) and foci ( ____, ____ ) and ( ____, ____ ).

To determine

To fill:

The blanks with appropriate answers.

Explanation

Given:

An graph of the equation x2b2+y2a2=1 with a>b>0 is an ellipse with vertices ( ____, ____ ) and ( ____, ____ ) and foci (0,±c), where c= __________. So the graph of x242+y252=1 is an ellipse with vertices ( ____, ____ ) and ( ____, ____ ) and foci ( ____, ____ ) and ( ____, ____ ).

Approach:

The basic equation for an ellipse with a horizontal major axis which is used is as follows,

x2b2+y2a2=1

Here, a and b are constant values.

Expression to find vertices is,

V=(0,±a)

Expression to find Foci is,

F=(0,±c),

Here, c2=a2b2

Calculation:

Consider the given equation of the ellipse,

x242+y252=1 ……(1)

Compare the above equation with the basic equation for an ellipse and find the vertices as follows,

a2=52a=±5

And,

b2=42b=±4

Find the vertices,

V=(0,±a)=(0,±5)=(0,5),(0,5)

Calculate the value of c as follows,

c2=a2b2c2=2516c2=9c=±3

Find the foci,

F=(0,±c)=(0,±3)=(0,3),(0,3)

Therefore, the vertices are (0,5),(0,5) and foci are (0,3),(0,3) and of the given equation of ellipse

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Chapter 12 Solutions

Show all chapter solutions add
Sect-12.1 P-11ESect-12.1 P-12ESect-12.1 P-13ESect-12.1 P-14ESect-12.1 P-15ESect-12.1 P-16ESect-12.1 P-17ESect-12.1 P-18ESect-12.1 P-19ESect-12.1 P-20ESect-12.1 P-21ESect-12.1 P-22ESect-12.1 P-23ESect-12.1 P-24ESect-12.1 P-25ESect-12.1 P-26ESect-12.1 P-27ESect-12.1 P-28ESect-12.1 P-29ESect-12.1 P-30ESect-12.1 P-31ESect-12.1 P-32ESect-12.1 P-33ESect-12.1 P-34ESect-12.1 P-35ESect-12.1 P-36ESect-12.1 P-37ESect-12.1 P-38ESect-12.1 P-39ESect-12.1 P-40ESect-12.1 P-41ESect-12.1 P-42ESect-12.1 P-43ESect-12.1 P-44ESect-12.1 P-45ESect-12.1 P-46ESect-12.1 P-47ESect-12.1 P-48ESect-12.1 P-49ESect-12.1 P-50ESect-12.1 P-51ESect-12.1 P-52ESect-12.1 P-53ESect-12.1 P-54ESect-12.1 P-55ESect-12.1 P-56ESect-12.1 P-57ESect-12.1 P-58ESect-12.1 P-59ESect-12.1 P-60ESect-12.1 P-61ESect-12.1 P-62ESect-12.1 P-63ESect-12.1 P-64ESect-12.1 P-65ESect-12.1 P-66ESect-12.2 P-1ESect-12.2 P-2ESect-12.2 P-3ESect-12.2 P-4ESect-12.2 P-5ESect-12.2 P-6ESect-12.2 P-7ESect-12.2 P-8ESect-12.2 P-9ESect-12.2 P-10ESect-12.2 P-11ESect-12.2 P-12ESect-12.2 P-13ESect-12.2 P-14ESect-12.2 P-15ESect-12.2 P-16ESect-12.2 P-17ESect-12.2 P-18ESect-12.2 P-19ESect-12.2 P-20ESect-12.2 P-21ESect-12.2 P-22ESect-12.2 P-23ESect-12.2 P-24ESect-12.2 P-25ESect-12.2 P-26ESect-12.2 P-27ESect-12.2 P-28ESect-12.2 P-29ESect-12.2 P-30ESect-12.2 P-31ESect-12.2 P-32ESect-12.2 P-33ESect-12.2 P-34ESect-12.2 P-35ESect-12.2 P-36ESect-12.2 P-37ESect-12.2 P-38ESect-12.2 P-39ESect-12.2 P-40ESect-12.2 P-41ESect-12.2 P-42ESect-12.2 P-43ESect-12.2 P-44ESect-12.2 P-45ESect-12.2 P-46ESect-12.2 P-47ESect-12.2 P-48ESect-12.2 P-49ESect-12.2 P-50ESect-12.2 P-51ESect-12.2 P-52ESect-12.2 P-53ESect-12.2 P-54ESect-12.2 P-55ESect-12.2 P-56ESect-12.2 P-57ESect-12.2 P-58ESect-12.2 P-59ESect-12.2 P-60ESect-12.2 P-61ESect-12.2 P-62ESect-12.2 P-63ESect-12.2 P-64ESect-12.2 P-65ESect-12.2 P-66ESect-12.2 P-67ESect-12.2 P-68ESect-12.2 P-69ESect-12.2 P-70ESect-12.2 P-71ESect-12.2 P-72ESect-12.3 P-1ESect-12.3 P-2ESect-12.3 P-3ESect-12.3 P-4ESect-12.3 P-5ESect-12.3 P-6ESect-12.3 P-7ESect-12.3 P-8ESect-12.3 P-9ESect-12.3 P-10ESect-12.3 P-11ESect-12.3 P-12ESect-12.3 P-13ESect-12.3 P-14ESect-12.3 P-15ESect-12.3 P-16ESect-12.3 P-17ESect-12.3 P-18ESect-12.3 P-19ESect-12.3 P-20ESect-12.3 P-21ESect-12.3 P-22ESect-12.3 P-23ESect-12.3 P-24ESect-12.3 P-25ESect-12.3 P-26ESect-12.3 P-27ESect-12.3 P-28ESect-12.3 P-29ESect-12.3 P-30ESect-12.3 P-31ESect-12.3 P-32ESect-12.3 P-33ESect-12.3 P-34ESect-12.3 P-35ESect-12.3 P-36ESect-12.3 P-37ESect-12.3 P-38ESect-12.3 P-39ESect-12.3 P-40ESect-12.3 P-41ESect-12.3 P-42ESect-12.3 P-43ESect-12.3 P-44ESect-12.3 P-45ESect-12.3 P-46ESect-12.3 P-47ESect-12.3 P-48ESect-12.3 P-49ESect-12.3 P-50ESect-12.3 P-51ESect-12.3 P-52ESect-12.3 P-53ESect-12.3 P-54ESect-12.3 P-55ESect-12.3 P-56ESect-12.3 P-57ESect-12.3 P-58ESect-12.3 P-59ESect-12.3 P-60ESect-12.4 P-1ESect-12.4 P-2ESect-12.4 P-3ESect-12.4 P-4ESect-12.4 P-5ESect-12.4 P-6ESect-12.4 P-7ESect-12.4 P-8ESect-12.4 P-9ESect-12.4 P-10ESect-12.4 P-11ESect-12.4 P-12ESect-12.4 P-13ESect-12.4 P-14ESect-12.4 P-15ESect-12.4 P-16ESect-12.4 P-17ESect-12.4 P-18ESect-12.4 P-19ESect-12.4 P-20ESect-12.4 P-21ESect-12.4 P-22ESect-12.4 P-23ESect-12.4 P-24ESect-12.4 P-25ESect-12.4 P-26ESect-12.4 P-27ESect-12.4 P-28ESect-12.4 P-29ESect-12.4 P-30ESect-12.4 P-31ESect-12.4 P-32ESect-12.4 P-33ESect-12.4 P-34ESect-12.4 P-35ESect-12.4 P-36ESect-12.4 P-37ESect-12.4 P-38ESect-12.4 P-39ESect-12.4 P-40ESect-12.4 P-41ESect-12.4 P-42ESect-12.4 P-43ESect-12.4 P-44ESect-12.4 P-45ESect-12.4 P-46ESect-12.4 P-47ESect-12.4 P-48ESect-12.4 P-49ESect-12.4 P-50ESect-12.4 P-51ESect-12.4 P-52ESect-12.4 P-53ESect-12.4 P-54ESect-12.4 P-55ESect-12.4 P-56ESect-12.4 P-57ESect-12.4 P-58ESect-12.4 P-59ESect-12.4 P-60ESect-12.4 P-61ESect-12.4 P-62ESect-12.4 P-63ESect-12.4 P-64ESect-12.4 P-65ESect-12.4 P-66ESect-12.4 P-67ESect-12.4 P-68ESect-12.5 P-1ESect-12.5 P-2ESect-12.5 P-3ESect-12.5 P-4ESect-12.5 P-5ESect-12.5 P-6ESect-12.5 P-7ESect-12.5 P-8ESect-12.5 P-9ESect-12.5 P-10ESect-12.5 P-11ESect-12.5 P-12ESect-12.5 P-13ESect-12.5 P-14ESect-12.5 P-15ESect-12.5 P-16ESect-12.5 P-17ESect-12.5 P-18ESect-12.5 P-19ESect-12.5 P-20ESect-12.5 P-21ESect-12.5 P-22ESect-12.5 P-23ESect-12.5 P-24ESect-12.5 P-25ESect-12.5 P-26ESect-12.5 P-27ESect-12.5 P-28ESect-12.5 P-29ESect-12.5 P-30ESect-12.5 P-31ESect-12.5 P-32ESect-12.5 P-33ESect-12.5 P-34ESect-12.5 P-35ESect-12.5 P-36ESect-12.5 P-37ESect-12.5 P-38ESect-12.5 P-39ESect-12.6 P-1ESect-12.6 P-2ESect-12.6 P-3ESect-12.6 P-4ESect-12.6 P-5ESect-12.6 P-6ESect-12.6 P-7ESect-12.6 P-8ESect-12.6 P-9ESect-12.6 P-10ESect-12.6 P-11ESect-12.6 P-12ESect-12.6 P-13ESect-12.6 P-14ESect-12.6 P-15ESect-12.6 P-16ESect-12.6 P-17ESect-12.6 P-18ESect-12.6 P-19ESect-12.6 P-20ESect-12.6 P-21ESect-12.6 P-22ESect-12.6 P-23ESect-12.6 P-24ESect-12.6 P-25ESect-12.6 P-26ESect-12.6 P-27ESect-12.6 P-28ESect-12.6 P-29ESect-12.6 P-30ESect-12.6 P-31ESect-12.6 P-32ESect-12.6 P-33ESect-12.6 P-34ESect-12.6 P-35ESect-12.6 P-36ESect-12.6 P-37ESect-12.6 P-38ESect-12.6 P-39ESect-12.6 P-40ESect-12.6 P-41ESect-12.6 P-42ESect-12.6 P-43ESect-12.6 P-44ESect-12.6 P-45ESect-12.6 P-46ESect-12.6 P-47ESect-12.CR P-1CCSect-12.CR P-2CCSect-12.CR P-3CCSect-12.CR P-4CCSect-12.CR P-5CCSect-12.CR P-6CCSect-12.CR P-7CCSect-12.CR P-8CCSect-12.CR P-1ESect-12.CR P-2ESect-12.CR P-3ESect-12.CR P-4ESect-12.CR P-5ESect-12.CR P-6ESect-12.CR P-7ESect-12.CR P-8ESect-12.CR P-9ESect-12.CR P-10ESect-12.CR P-11ESect-12.CR P-12ESect-12.CR P-13ESect-12.CR P-14ESect-12.CR P-15ESect-12.CR P-16ESect-12.CR P-17ESect-12.CR P-18ESect-12.CR P-19ESect-12.CR P-20ESect-12.CR P-21ESect-12.CR P-22ESect-12.CR P-23ESect-12.CR P-24ESect-12.CR P-25ESect-12.CR P-26ESect-12.CR P-27ESect-12.CR P-28ESect-12.CR P-29ESect-12.CR P-30ESect-12.CR P-31ESect-12.CR P-32ESect-12.CR P-33ESect-12.CR P-34ESect-12.CR P-35ESect-12.CR P-36ESect-12.CR P-37ESect-12.CR P-38ESect-12.CR P-39ESect-12.CR P-40ESect-12.CR P-41ESect-12.CR P-42ESect-12.CR P-43ESect-12.CR P-44ESect-12.CR P-45ESect-12.CR P-46ESect-12.CR P-47ESect-12.CR P-48ESect-12.CR P-49ESect-12.CR P-50ESect-12.CR P-51ESect-12.CR P-52ESect-12.CR P-53ESect-12.CR P-54ESect-12.CR P-55ESect-12.CR P-56ESect-12.CR P-57ESect-12.CR P-58ESect-12.CR P-59ESect-12.CR P-60ESect-12.CR P-61ESect-12.CR P-62ESect-12.CR P-63ESect-12.CR P-64ESect-12.CR P-65ESect-12.CR P-66ESect-12.CR P-67ESect-12.CR P-68ESect-12.CR P-69ESect-12.CR P-70ESect-12.CR P-71ESect-12.CR P-72ESect-12.CR P-73ESect-12.CR P-74ESect-12.CR P-75ESect-12.CR P-76ESect-12.CR P-77ESect-12.CR P-78ESect-12.CR P-79ESect-12.CR P-80ESect-12.CT P-1CTSect-12.CT P-2CTSect-12.CT P-3CTSect-12.CT P-4CTSect-12.CT P-5CTSect-12.CT P-6CTSect-12.CT P-7CTSect-12.CT P-8CTSect-12.CT P-9CTSect-12.CT P-10CTSect-12.CT P-11CTSect-12.CT P-12CTSect-12.CT P-13CTSect-12.CT P-14CTSect-12.CT P-15CTSect-12.CT P-16CTSect-12.CT P-17CTSect-12.FOM P-1PSect-12.FOM P-2PSect-12.FOM P-3PSect-12.FOM P-4PSect-12.FOM P-5PSect-12.FOM P-6P