/*! 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 72 How can you distinguish an ellip... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 72

How can you distinguish an ellipse from a hyperbola by looking at their equations?

Short Answer

Expert verified
The equations of an ellipse and a hyperbola can be distinguished by looking at the signs of the terms. In ellipse equation all terms are added together, whereas in a hyperbola equation one term is subtracted from the other.

Step by step solution

01

Understand the Equations

The general form of equation for an ellipse in standard form is \( \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1 \) and for a hyperbola it is \( \frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1 \) or \( \frac{(y-k)^2}{b^2} - \frac{(x-h)^2}{a^2} = 1 \). The variables \( h \) and \( k \) are the coordinates of the center of the ellipse or the hyperbola. The variables \( a \) and \( b \) determine the shape of the ellipse and hyperbola.
02

Identify the Difference

In an ellipse, all terms are added together while in a hyperbola, one term is subtracted from the other. This is the main distinguishing factor when comparing equations of an ellipse and a hyperbola.
03

Summary

If all terms in the equation are positive, it defines an ellipse. If one term is subtracted from the other, it defines a hyperbola.

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

Describe how to graph \(\frac{x^{2}}{25}+\frac{y^{2}}{16}=1\)

In Exercises \(67-68,\) graph each semiellipse. $$ y=-\sqrt{16-4 x^{2}} $$

Will help you prepare for the material covered in the first section of the next chapter. Evaluate \(j^{2}+1\) for all consecutive integers from 1 to 6 inclusive. Then find the sum of the six evaluations.

The towers of the Golden Gate Bridge connecting San Francisco to Marin County are 1280 meters apart and rise 160 meters above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. What is the height of the cable 200 meters from a tower? Round to the nearest meter.

Identify the conic and write its equation in rectangular coordinates: \(r=\frac{1}{2-2 \cos \theta}\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Statistics

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.