Solution
The center is at (4, 5), and the hyperbola is horizontal. We have
a
= 3 and
b
= 2, so the vertices are (4 ± 3, 5), or (7, 5) and (1, 5). We can sketch the hyperbola more readily if we can draw a fundamental rectangle. Using (4, 5
In this example, since
a
= 3 and
b
= 2, we draw a rectangle 2
a
= 6 units wide and 2
b
= 4 units high with a center at (4, 5). We draw extended diagonals through the rectangle. From the vertex at (7, 5), we draw a branch of the hyperbol
Student Practice 3
Graph
open parenthesis y plus 2 close parenthesis to the 2 power over 9
−
open parenthesis x
−
3 close parenthesis to the 2 power over 16 equals 1.
Page 40 of 64
Print | Beginning & Intermediate Algebra
1/31/2014
...

PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.
Graphing Calculator
Exploration
Graph the hyperbola in Example 3 using
y sub 1 equals 5 plus the square root of 4 open parenthesis x
−
4 close parenthesis to the 2 power over 9
−
4 end radicand
and
y sub 2 equals 5
−
the square root of 4 open parenthesis x
−
4 close parenthesis to the 2 power over 9
−
4 end radicand
Do you see how we obtained
y
1
and
y
2
?
658659
10.4 Exercises: Verbal and Writing Skills, Exercises 1–4
1.What is the standard form of the equation of a horizontal hyperbola centered at the origin?2.What are the vertices of the hyperbola Is this a horizontal hyperbola or a vertical hyperbola? Why?3.Explain in your own words how you would draw the graph of the hyperbola 4.Explain how you determine the center of the hyperbola Find the vertices and graph each hyperbola. If the equation is not in standard form, write it as such.
.
.
5.
6.
Page 41 of 64
Print | Beginning & Intermediate Algebra
1/31/2014
...

PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.
7.
8.
9.
4
x
2
−
y
2
= 64
Page 42 of 64
Print | Beginning & Intermediate Algebra
1/31/2014
...

PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.
10.
x
2
−
4
y
2
= 4
659660
11.
8
x
2
−
y
2
= 16
12.
12
x
2
−
y
2
= 36
13.
4
y
2
−
3
x
2
= 48
Page 43 of 64
Print | Beginning & Intermediate Algebra
1/31/2014
...

PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.

#### You've reached the end of your free preview.

Want to read all 64 pages?

- Fall '13
- Quadratic equation, Conic section