Skip to content Skip to navigation Skip to collection information

OpenStax_CNX

You are here: Home » Content » Advanced Algebra II: Activities and Homework » Homework: Ellipses

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This collection is included inLens: Connexions Featured Content
    By: Connexions

    Comments:

    "This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Busbee's Math Materials display tagshide tags

    This collection is included inLens: Busbee's Math Materials Lens
    By: Kenneth Leroy Busbee

    Click the "Busbee's Math Materials" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Homework: Ellipses

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides homework problems related to ellipses.

Exercise 1

In class, we discussed how to draw an ellipse using a piece of cardboard, two thumbtacks, a string, and a pen or marker. Do this. Bring your drawing in as part of your homework. (Yes, this is a real part of your homework!)

Exercise 2

( x - 2 ) 2 9 + y 2 ( 1 4 ) = 1 ( x - 2 ) 2 9 + y 2 ( 1 4 ) =1

  • a. Is it horizontal or vertical?
  • b. What is the center?
  • c. What is aa?
  • d. What is bb?
  • e. What is cc?
  • f. Graph it.

Exercise 3

4 x 2 9 + 25 y 2 = 1 4 x 2 9 +25 y 2 =1

This sort of looks like an ellipse in standard form, doesn’t it? It even has a 1 on the right. But it isn’t. Because we have no room in our standard form for that 4 and that 25—for numbers multiplied by the x2 and y2 terms. How can we get rid of them, to get into standard form, while retaining the 1 on the right?

  • a. Rewrite the left-hand term, 4 x 2 9 4 x 2 9 , by dividing the top and bottom of the fraction by 4. Leave the bottom as a fraction; don't make it a decimal.
  • b. Rewrite the right-hand term, 25 y 2 25 y 2 , by dividing the top and bottom of the fraction by 25. Leave the bottom as a fraction; don't make it a decimal.
  • c. Now, you're in standard form. what is the center?
  • d. How long is the major axis?
  • e. How long is the minor axis?
  • f. What are the coordinated of the two foci?
  • g. Graph it.

Exercise 4

18 x 2 + 1 2 y 2 + 108 x + 5 y + 170 = 0 18 x 2 + 1 2 y 2 +108x+5y+170=0

  • a. Put in standard form.
  • b. Is it horizontal or vertical?
  • c. What is the center?
  • d. How long is the major axis?
  • e. How long is the minor axis?
  • f. What are the coordinates of the two foci?
  • g. Graph it.

Exercise 5

The major axis of an ellipse runs from (5,-6) to (5,12). One focus is at (5,-2). Find the equation for the ellipse.

Exercise 6

The foci of an ellipse are at (-2,3) and (2,3) and the ellipse contains the origin. Find the equation for the ellipse.

Exercise 7

We traditionally say that the Earth is 93 million miles away from the sun. However, if it were always 93 million miles away, that would be a circle (right?). In reality, the Earth travels in an ellipse, with the sun at one focus. According to one Web site I found,

There is a 6% difference in distance between the time when we're closest to the sun (perihelion) and the time when we're farthest from the sun (aphelion). Perihelion occurs on January 3 and at that point, the earth is 91.4 million miles away from the sun. At aphelion, July 4, the earth is 94.5 million miles from the sun. [source]

Write an equation to describe the orbit of the Earth around the sun. Assume that it is centered on the origin and that the major axis is horizontal. (*Why not? There are no axes in space, so you can put them wherever it is most convenient.) Also, work in units of millions of miles—so the numbers you are given are simply 91.4 and 94.5.

Figure 1
A picture illustrating the orbit of Earth around the sun.

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks