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Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2011 China Second Round Olympiad
7
parabola
parabola
Source: 0
January 30, 2012
conics
parabola
analytic geometry
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Problem Statement
The line
x
−
2
y
−
1
=
0
x-2y-1=0
x
−
2
y
−
1
=
0
insects the parabola
y
2
=
4
x
y^2=4x
y
2
=
4
x
at two different points
A
,
B
A, B
A
,
B
. Let
C
C
C
be a point on the parabola such that
∠
A
C
B
=
π
2
\angle ACB=\frac{\pi}{2}
∠
A
CB
=
2
π
. Find the coordinate of point
C
C
C
.
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