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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 10.1, Problem 44E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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By definition, a hyperbola is the locus of points whose positive difference of distances from two fixed points F 1 and F 2 (called foci) is constant. In the grid provided, find points whose difference of distances from points F 1 5, 0 and F 2 - 5, 0 is 6. That is, locate some points for which P F 1 - P F 2 = 6 or P F 2 - P F 1 = 6 ; point P 3, 0 is one such point. Then sketch the hyperbola.

Chapter 10.1, Problem 44E, By definition, a hyperbola is the locus of points whose positive difference of distances from two

To determine

To sketch:

The hyperbola using the given data.

Explanation

The general equation of the hyperbola is shown below.

x2a2-y2b2=1

Vertices ±a, 0.

Foci ±c, 0

Here c2=a2+b2

The foci of the hyperbola is F15, 0 and F2-5, 0.

Since, foci ±c, 0

Hence, c=5

In the problem, it is given that one point is 3, 0.

Vertices ±a, 0

The other point is -3, 0.

Since PF1-PF2=6

2a=6

Dividing by 2,

2a2=62

From this,

a=3

Using the values of a and c, we have to find b

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