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MAA AMC
AMC 12/AHSME
1984 AMC 12/AHSME
22
22
Part of
1984 AMC 12/AHSME
Problems
(1)
Interesting set of points by t
Source:
10/24/2005
Let
a
a
a
and
c
c
c
be fixed positive numbers. For each real number
t
t
t
let
(
x
t
,
y
t
)
(x_t, y_t)
(
x
t
,
y
t
)
be the vertex of the parabola
y
=
a
x
2
+
b
x
+
c
y = ax^2+bx+c
y
=
a
x
2
+
b
x
+
c
. If the set of vertices
(
x
t
,
y
t
)
(x_t, y_t)
(
x
t
,
y
t
)
for all real values of
t
t
t
is graphed in the plane, the graph is A. a straight line B. a parabola C. part, but not all, of a parabola D. one branch of a hyperbola E. None of these
conics
parabola
hyperbola