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Putnam
1941 Putnam
A5
A5
Part of
1941 Putnam
Problems
(1)
Putnam 1941 A5
Source: Putnam 1941
2/23/2022
The line
L
L
L
is parallel to the plane
y
=
z
y=z
y
=
z
and meets the parabola
2
x
=
y
2
,
z
=
0
2x=y^2 ,z=0
2
x
=
y
2
,
z
=
0
and the parabola
3
x
=
z
2
,
y
=
0
3x=z^2, y=0
3
x
=
z
2
,
y
=
0
. Prove that if
L
L
L
moves freely subject to these constraints then it generates the surface
x
=
(
y
−
z
)
(
y
2
−
z
3
)
x=(y-z)\left(\frac{y}{2}-\frac{z}{3}\right)
x
=
(
y
−
z
)
(
2
y
−
3
z
)
.
Putnam
conics
parabola