romasko (qrr58) – Assignment 3 – luecke – (55035)
1
This
printout
should
have
10
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
001
10.0 points
Classify the quadric surface
x
z
y
1.
elliptic paraboloid
2.
hyperbolic paraboloid
3.
twosheeted hyperboloid
correct
4.
elliptic cone
5.
onesheeted hyperboloid
6.
ellipsoid
Explanation:
The trace on any horizontal plane,
i.e.,
any
plane parallel to the coordinate plane
z
=
c
,
is always a circle for all

c
 ≤
c
0
for some
choice of
c
0
, while the trace on any plane
parallel to the coordinate planes
x
= 0 and
y
= 0 is alway a hyperbolas.
Consequently
the quadric surface is a
twosheeted hyperboloid
.
keywords:
quadric surface, ellipsoid, ellip
tic paraboloid, hyperbolic paraboloid, one
sheeted
hyperboloid,
twosheeted
hyper
boloid,
002
10.0 points
Which one of the following equations has
graph
when the circular cylinder has radius 2.
1.
y
2
+
z
2

4
y
= 0
correct
2.
x
2
+
y
2

2
x
= 0
3.
x
2
+
y
2
+ 4
y
= 0
4.
y
2
+
z
2

2
y
= 0
5.
x
2
+
y
2
+ 2
y
= 0
6.
x
2
+
y
2

4
x
= 0
Explanation:
The graph is a circular cylinder whose axis
of symmetry is parallel to the
x
axis, so it
will be the graph of an equation containing no
x
term. This already eliminates the equations
x
2
+
y
2
+ 2
y
= 0
,
x
2
+
y
2
+ 4
y
= 0
,
x
2
+
y
2

2
x
= 0
,
x
2
+
y
2

4
x
= 0
.
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 Fall '07
 Gilbert
 Hyperboloid, Ellipsoid, Quadric, Paraboloid

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