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Putnam
1942 Putnam
B2
B2
Part of
1942 Putnam
Problems
(1)
Putnam 1942 B2
Source: Putnam 1942
3/1/2022
For the family of parabolas
y
=
a
3
x
2
3
+
a
2
x
2
−
2
a
y= \frac{ a^3 x^{2}}{3}+ \frac{ a^2 x}{2}-2a
y
=
3
a
3
x
2
+
2
a
2
x
−
2
a
(i) find the locus of vertices, (ii) find the envelope, (iii) sketch the envelope and two typical curves of the family.
Putnam
conics
parabola