/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 76 Describe one similarity and one ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 76

Describe one similarity and one difference between the graphs of \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\) and \(\frac{x^{2}}{16}+\frac{y^{2}}{25}=1\)

Short Answer

Expert verified
The similarity between the two graphs is that both have their centers at the origin and share identical lengths of axes. However, their difference lies in their orientation, as one is stretched along the x-axis (first ellipse) while the other one is stretched along the y-axis (second ellipse).

Step by step solution

01

Identifying the Ellipses

First, let's identify the given ellipses from their given standard form. The first ellipse is defined by the equation \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\) which shows that the semi-major axis is along the x-axis (a=5) and the semi-minor axis is along the y-axis (b=4). The second ellipse is defined by the equation \(\frac{x^{2}}{16}+\frac{y^{2}}{25}=1\) which shows that the semi-major axis is along the y-axis (b=5) and the semi-minor axis is along the x-axis (a=4).
02

Finding Similarities

From the equations, it is visible that both ellipses have the same center which is the origin (0,0). Moreover, the lengths of their axes are equal but interchanged. Both have their major axis of length 10 and minor axis of length 8.
03

Finding Differences

The primary difference lies in the orientation of the ellipses. In the first ellipse, the semi-major axis is along the x-axis, which means the ellipse is stretched more along the x-axis. On the other side, for the second ellipse, the semi-major axis is along the y-axis, indicating that this ellipse is stretched more along the y-axis.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What is an ellipse?

Where possible, find each product. a. \(\left[\begin{array}{rr}{1} & {0} \\ {0} & {-1}\end{array}\right]\left[\begin{array}{rr}{-1} & {0} \\ {0} & {-1}\end{array}\right]\) b. \(\left[\begin{array}{rr}{-1} & {0} \\ {0} & {-1}\end{array}\right]\left[\begin{array}{rrr}{-1} & {0} & {1} \\ {0} & {-1} & {1}\end{array}\right]\)

In each exercise, graph the equation in a rectangular coordinate system. $$y=\frac{1}{2} x^{2}+1, x \geq 0$$

Solve by eliminating variables: $$\left\\{\begin{aligned} x-6 y &=-22 \\ 2 x+4 y-3 z &=29 \\ 3 x-2 y+5 z &=-17 \end{aligned}\right.$$

Verify the identity: $$ \sin \left(\frac{3 \pi}{2}-x\right)=-\cos x $$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.