This preview shows pages 1–2. Sign up to view the full content.
romasko (qrr58) – Assignment 3 – luecke – (55035)
1
This printout should have 10 questions.
Multiplechoice questions may continue on
the next column or page – fnd 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
.
On the other hand, the intersection oF the
graph with the
yz
plane,
i.e.
the
x
= 0 plane,
is a circle centered on the
y
axis and passing
through the origin as shown in
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '07
 Gilbert

Click to edit the document details