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Swedish Mathematical Competition
2002 Swedish Mathematical Competition
3
3
Part of
2002 Swedish Mathematical Competition
Problems
(1)
y = ax^2, intersect circle ((0,0),1) besides (0, 0)
Source: 2002 Swedish Mathematical Competition p3
3/21/2021
C
C
C
is the circle center
(
0
,
1
)
(0,1)
(
0
,
1
)
, radius
1
1
1
.
P
P
P
is the parabola
y
=
a
x
2
y = ax^2
y
=
a
x
2
. They meet at
(
0
,
0
)
(0, 0)
(
0
,
0
)
. For what values of
a
a
a
do they meet at another point or points?
parabola
system of equations
System
parameter
algebra
analytic geometry