/*! 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} Q. 59 Prove that for an ellipse or a h... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Q. 59 (page 773)

Prove that for an ellipse or a hyperbola the eccentricity is given by

e=the distance between the focithe distance between the vertices

Short Answer

Expert verified

Hence proved.

Step by step solution

01

Step 1. Given information.

We are given,

e=the distance between the focithe distance between the vertices

02

Step 2. Explanation.

Now,

Let the foci of the ellipse are卤A2-B2,0.Formula for the distance=x1-x22+y1-y22Distance=A2-B2--A2-B22+(0-0)2Distance=2A2-B22Thus the distance between the foci is,Distance=2A2-B2Wehavetheeccentricitye=A2-B2AThene=2A2-B22AThus,e=the distance between focithe distance between the vertices

Hence proved.

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

In Exercises 32鈥�47 convert the equations given in polar coordinates to rectangular coordinates.

r=tan胃

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.

foci(卤伪,0), major axis4伪

Use Cartesian coordinates to express the equations for the hyperbolas determined by the conditions specified in Exercises 38鈥�43.

foci(3,1)and(3,9), directrixy=4

Explain why there are infinitely many different ellipses with the same foci.

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

directrixx=-1,focus(2,5)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Decision Maths

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.