Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Question

Chapter 10.3, Problem 9CFU

To determine

To find: For the ellipse 25x2+9y2+100x−18y=116 , the coordinates of the center, foci and vertices. Then graph the equation.

Expert Solution & Answer

Answer to Problem 9CFU

Center(−2,1)Vertices:(1,1),(−5,1),(−2,6),(−2,−4)foci:(−2,1±4)The graph

Explanation of Solution

Given information: 25x2+9y2+100x−18y=116

Calculation:

25x2+9y2+100x−18y=116

Group terms, factor and set up to complete square.

25(x2+4x−−)+9(y2−2y−−)=116

Add (12b)2(constant) to both sides, b=4,−2 respectively.

25(x2+4x+4)+9(y2−2y+1)=116+25(4)+9(1)

Factor both terms

25(x+2)2+9(y−1)2=225

Divide both sides by 225.

(x+2)29+(y−1)225=1

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.3, Problem 9CFU

Center:(−2,1)vertices:(1,1),(−5,1),(−2,6),(−2,−4)foci→25−9=c2→c=4foci:(−2,1±4)

Chapter 10.3, Problem 8CFU

Chapter 10.3, Problem 10CFU

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 10.1 - Prob. 1CFU Ch. 10.1 - Prob. 2CFU Ch. 10.1 - Prob. 3CFU Ch. 10.1 - Prob. 4CFU Ch. 10.1 - Prob. 5CFU Ch. 10.1 - Prob. 6CFU Ch. 10.1 - Prob. 7CFU Ch. 10.1 - Prob. 8CFU Ch. 10.1 - Prob. 9CFU Ch. 10.1 - Prob. 10CFU

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