Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Chapter 9.4, Problem 19WE
To determine

To calculate: To write the equation of ellipse having the given points as foci and the given number as the sum of focal radii

Expert Solution & Answer
Check Mark

Answer to Problem 19WE

Equation of ellipse is x281+y245=1

Explanation of Solution

Given information: Foci are (6,0),(6,0) and sum of focal radii 18

Formula Used:

Standard form of the equation of ellipse with center (h,k) and major axis parallel to x-axis is:

  (xh)2a2+(yk)2b2=1

Where, a= x-intercept, b= y-intercept, c2=a2b2

When, a>b , foci lies on x-axis and coordinates of foci are (h±c,k)

When b>a , foci lies on y-axis and coordinates of foci are (h,k±c)

Calculation:

Given the Foci as follows (6,0),(6,0)

Thus, c=±6

Also, given the sum of focal radii 18

  2a=18a=182a=9

Now, b is calculated using the below formula:

  c2=a2b2

Substituting the values:

  b2=a2c2b2=9262b2=8136b2=45b=±35

Equation of ellipse is given as follows:

  (xh)2a2+(yk)2b2=1 :

Substituting the values:

  (x0)2(9)2+(y0)2(±35)2=1x281+y245=1

Conclusion:

Hence, equation of ellipse is x281+y245=1

Chapter 9 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 9.1 - Prob. 11OECh. 9.1 - Prob. 12OECh. 9.1 - Prob. 13OECh. 9.1 - Prob. 14OECh. 9.1 - Prob. 15OECh. 9.1 - Prob. 1WECh. 9.1 - Prob. 2WECh. 9.1 - Prob. 3WECh. 9.1 - Prob. 4WECh. 9.1 - Prob. 5WECh. 9.1 - Prob. 6WECh. 9.1 - Prob. 7WECh. 9.1 - Prob. 8WECh. 9.1 - Prob. 9WECh. 9.1 - Prob. 10WECh. 9.1 - Prob. 11WECh. 9.1 - Prob. 12WECh. 9.1 - Prob. 13WECh. 9.1 - Prob. 14WECh. 9.1 - Prob. 15WECh. 9.1 - Prob. 16WECh. 9.1 - Prob. 17WECh. 9.1 - Prob. 18WECh. 9.1 - Prob. 19WECh. 9.1 - Prob. 20WECh. 9.1 - Prob. 21WECh. 9.1 - Prob. 22WECh. 9.1 - Prob. 23WECh. 9.1 - Prob. 24WECh. 9.1 - Prob. 25WECh. 9.1 - Prob. 26WECh. 9.1 - Prob. 27WECh. 9.1 - Prob. 28WECh. 9.1 - Prob. 29WECh. 9.1 - Prob. 30WECh. 9.1 - Prob. 31WECh. 9.1 - Prob. 32WECh. 9.1 - Prob. 1PCh. 9.1 - Prob. 2PCh. 9.1 - Prob. 3PCh. 9.1 - Prob. 4PCh. 9.1 - Prob. 5PCh. 9.1 - Prob. 6PCh. 9.1 - Prob. 7PCh. 9.1 - Prob. 8PCh. 9.1 - Prob. 9PCh. 9.1 - Prob. 10PCh. 9.1 - Prob. 11PCh. 9.1 - Prob. 12PCh. 9.1 - Prob. 13PCh. 9.1 - Prob. 14PCh. 9.1 - Prob. 1MRECh. 9.1 - 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Prob. 7WECh. 9.6 - Prob. 8WECh. 9.6 - Prob. 9WECh. 9.6 - Prob. 10WECh. 9.6 - Prob. 11WECh. 9.6 - Prob. 12WECh. 9.6 - Prob. 13WECh. 9.6 - Prob. 14WECh. 9.6 - Prob. 15WECh. 9.6 - Prob. 16WECh. 9.6 - Prob. 17WECh. 9.6 - Prob. 18WECh. 9.6 - Prob. 19WECh. 9.6 - Prob. 20WECh. 9.6 - Prob. 21WECh. 9.6 - Prob. 1STCh. 9.6 - Prob. 2STCh. 9.6 - Prob. 3STCh. 9.6 - Prob. 4STCh. 9.6 - Prob. 5STCh. 9.6 - Prob. 6STCh. 9.7 - Prob. 1OECh. 9.7 - Prob. 2OECh. 9.7 - Prob. 3OECh. 9.7 - Prob. 4OECh. 9.7 - Prob. 5OECh. 9.7 - Prob. 6OECh. 9.7 - Prob. 7OECh. 9.7 - Prob. 8OECh. 9.7 - Prob. 9OECh. 9.7 - Prob. 10OECh. 9.7 - Prob. 11OECh. 9.7 - Prob. 12OECh. 9.7 - Prob. 1WECh. 9.7 - Prob. 2WECh. 9.7 - Prob. 3WECh. 9.7 - Prob. 4WECh. 9.7 - Prob. 5WECh. 9.7 - Prob. 6WECh. 9.7 - Prob. 7WECh. 9.7 - Prob. 8WECh. 9.7 - Prob. 9WECh. 9.7 - Prob. 10WECh. 9.7 - Prob. 11WECh. 9.7 - Prob. 12WECh. 9.7 - Prob. 13WECh. 9.7 - Prob. 14WECh. 9.7 - Prob. 15WECh. 9.7 - Prob. 16WECh. 9.7 - Prob. 17WECh. 9.7 - Prob. 18WECh. 9.7 - Prob. 19WECh. 9.7 - Prob. 20WECh. 9.7 - Prob. 1MRECh. 9.7 - Prob. 2MRECh. 9.7 - Prob. 3MRECh. 9.7 - Prob. 4MRECh. 9.7 - Prob. 5MRECh. 9.7 - Prob. 6MRECh. 9.7 - Prob. 7MRECh. 9.8 - Prob. 1OECh. 9.8 - Prob. 2OECh. 9.8 - Prob. 3OECh. 9.8 - Prob. 1WECh. 9.8 - Prob. 2WECh. 9.8 - Prob. 3WECh. 9.8 - Prob. 4WECh. 9.8 - Prob. 5WECh. 9.8 - Prob. 6WECh. 9.8 - Prob. 7WECh. 9.8 - Prob. 8WECh. 9.8 - Prob. 9WECh. 9.8 - Prob. 10WECh. 9.8 - Prob. 11WECh. 9.8 - Prob. 12WECh. 9.8 - Prob. 13WECh. 9.8 - Prob. 14WECh. 9.8 - Prob. 15WECh. 9.8 - Prob. 16WECh. 9.8 - Prob. 17WECh. 9.8 - Prob. 18WECh. 9.8 - Prob. 19WECh. 9.8 - Prob. 20WECh. 9.8 - Prob. 21WECh. 9.8 - Prob. 22WECh. 9.8 - Prob. 23WECh. 9.8 - Prob. 24WECh. 9.8 - Prob. 25WECh. 9.8 - Prob. 26WECh. 9.8 - Prob. 1PCh. 9.8 - Prob. 2PCh. 9.8 - Prob. 3PCh. 9.8 - Prob. 4PCh. 9.8 - Prob. 5PCh. 9.8 - Prob. 6PCh. 9.8 - Prob. 7PCh. 9.8 - Prob. 8PCh. 9.8 - Prob. 9PCh. 9.8 - Prob. 10PCh. 9.8 - Prob. 11PCh. 9.8 - Prob. 12PCh. 9.8 - Prob. 13PCh. 9.8 - Prob. 14PCh. 9.9 - Prob. 1OECh. 9.9 - 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What is Ellipse?; Author: Don't Memorise;https://www.youtube.com/watch?v=nzwCInIMlU4;License: Standard YouTube License, CC-BY