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system S
such that ecoref and paramet
ISAF
iiiiiifii
the surface
revolution about
the new axisofOZ
t
70
Newreference system S such that
01
If Etzionofline l
9 0,0
Efp
whereP Q are 2 point
0 9,00
P 10 9,0
of
Hence
l
ez
forexample
Él
forexample en10,0 1
1 1,0
ej es x ej
es sez
Hence
S 119,90
Parameterization
of
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in
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n s
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revolution in si
the
surface
of
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test t sint 9 DE 9
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The
the surfaces
curve lies on
4
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ya_tuit 46 441 4
If
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x
y
TECA GAGE Gray
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P
if Gray
QMHEGncy
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z
Y
4
since
Hence
Y
cylinder
aplindrid
y
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sint
y
y
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EL
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on
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C
gen
orthonormal basis formed
equation
fer es
by eigenvectors
of Prz.IT inthe reference systemSECO
1
HEIKE
P
er er
ins
P in S
una.JP
where
4g
and of
Hence
f f tiftp.ltj
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Ix y
tl
D.P yY
o
1
o
y
Mt dothecalculations
p
j
P isthe change of basis
because
a orthonormal basis formed
of
byeigenvectors of eigenvalues 1 and3
matrix
therefore
theequation in S
Mt 3 y
step
3
y
is
0
11
complete the squares
4
y
3
3
ly
14 2 si
We consider
obtained
Fray 3
this Case
yi 2 fh.gl
system
SE LO
by changingthe origin soHeat
Hit II
3 y 2zz.y
fly Irt Er
FEI
a new reference
in
y
nena
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er er
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and
Theequation ofthe conic in the new referencesystems is
3y
2
3yaa
22
3
1
0
andthis is
an ellipse
Era
that cambe parameterized
g
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The implicitequation
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eliminate z
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3434 4464 9
3 2 242 6g 9
0
215341 9
0
342
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y
complete squares
44
31212941
9 0
38 219 31212912 9
3
9 0
0
424 312 7 divide by271to have1
independent term
EIIa
the projection
Hence
tonto
of
Parametrization
is an ellipse
East
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te CORTA
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Parametrization
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Consider C
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Parameleizethecone C fromtheparametrization
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We want parametrization of Ca n 5
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of
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parametrization
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px toe 0,21 for a genericpoint Ht ofC
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FÉÉÉÉFÍÜEÉ
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5L
Question
It
is
what istheprojectingcylinderCzofc
the plane Xy l and the circle
can be parameenzed
iPEEEI.EE FEED
withthis parametrization thetangent vectordoes notexistfor10,1ol s0,0
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