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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Question

Chapter 10.3, Problem 50E

(a)

To determine

To develop:A formula for the area of an ellipse with equation x2a2+y2b2=1 . The area of a circle with equation x2+y2=r2 is πr2

(a)

Expert Solution

Answer to Problem 50E

π(a×b)

Explanation of Solution

Given information: Geometry: The Square has an area of 1 square unit. If the square is stretched horizontally by a factor of a and compressed vertically by a factor of b , the area of the rectangle formed is ab square units.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.3, Problem 50E , additional homework tip 1

Calculation:

Comparing the area of the square (L×W) to the circle,

You see you can write the circle as π(r×r) ,

As you stretch the circle out,

You get instead π(a×b) for the area of the ellipse.

(b)

To determine

To find:The area of the ellipse x29+y24=1 , using the formula found in part a.

(b)

Expert Solution

Answer to Problem 50E

Area = 6π

Explanation of Solution

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.3, Problem 50E , additional homework tip 2

Calculation:

a=3,b=2

So the area of the ellipse is:

Area=π(3×2)Area=6π

Chapter 10.3, Problem 49E

Chapter 10.3, Problem 51E

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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