Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 44E
Related questions
Question
19 please
Transcribed Image Text:I
V
840
III
11-20 Use traces to sketch and identify the surface.
11. x = y² + 4z²
13. x² = 4y² + z²
15. 9y² + 4z² = x² + 36
x²
y²
72
+==1
4
9
25
16,702 901
=
10. (a) Find and identify the traces of the quadric surface
-x² - y² + z²
1 and explain why the graph looks like
the graph of the hyperboloid of two sheets in Table 1.
(b) If the equation in part (a) is changed to x² - y² - z² = 1,
what happens to the graph? Sketch the new graph.
17.
VII
19. y = z² - x²
21-28 Match the equation with its graph (labeled I-VIII). Give
reasons for your choice.
21. x² + 4y² + 9z² = 1
23. x² - y² + z² = 1
25. y = 2x² + z²
27. x² + 2z² = 1
+
x
XA
CHAPTER 12 Vectors and the Geometry of Space
X
ZA
ZA
orxat 142 biolog
ZA
ZA
y
y
y
nbsup
GOTS out vitw
II
IV
y
4 biolodisqyt
VI
12. 4x² +9y² + 9z² = 36
14. z² - 4x² - y² = 4
16. 3x² + y + 3z² = 0
18. 3x² - y² + 3z² = 0
no sit
20. x = y² = z²
22. 9x² + 4y² + z² = 1
24. x² + y² - z² = 1
26. y² = x² + 2z²
28. y = x² - z²
VIII
ampo
XX
bne
$007
X
XK
ZA
Z
ZA
N
XXX
20 y
nu bakt
y
y
traces shown.
29-30 Sketch and identify a quadric surface that could have the
29. Traces in x = k
k = ±2
k = ±1
30. Traces in x = k
Z
k = 0
An
in 301
od odr
y
k = ±2
k = ±1
k=0
y
Traces in y = k
39.-4x² - y² + z² = 1
41. -4x² - y² + z² = 0
k=2
k=1
ZA
k=0
Traces in z = k
k=0
k=-1
k=0
YA
k=-2
31-38 Reduce the equation to one of the standard forms, classify
the surface, and sketch it.
31. y² = x² + z²
33. x² + 2y = 2z² = 0
35. x² + y² - 2x - 6y - z + 10 = 0
36. x² - y² - z² - 4x − 2z + 3 = 0
on lo sode adi
37. x² - y² + z² - 4x = 2z = 0
38. 4x² + y² + z² - 24x - 8y + 4z +55 = 0
CORSKI
k = 2
32. 4x² - y + 2z² = 0
34. y² = x² + 4z² +4
10
39-42 Use a computer with three-dimensional graphing soft-
ware to graph the surface. Experiment with viewpoints and with
domains for the variables until you get a good view of the surface
40. x² - y² -z = 0
42. x² - 6x + 4y² - z=0
43. Sketch the region bounded by the surfaces z = √√√x² + y²
and x² + y² = 1 for 1 ≤ z ≤ 2.
bra
slina
44. Sketch the region bounded by the paraboloids z = x² + y²
and z = 2 - x² - y².
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