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Bulgaria National Olympiad
1990 Bulgaria National Olympiad
Problem 2
Problem 2
Part of
1990 Bulgaria National Olympiad
Problems
(1)
parabola y=ax^2, OA _|_ OB
Source: Bulgaria 1990 P2
6/9/2021
Let be given a real number
α
≠
0
\alpha\ne0
α
=
0
. Show that there is a unique point
P
P
P
in the coordinate plane, such that for every line through
P
P
P
which intersects the parabola
y
=
α
x
2
y=\alpha x^2
y
=
α
x
2
in two distinct points
A
A
A
and
B
B
B
, segments
O
A
OA
O
A
and
O
B
OB
OB
are perpendicular (where
O
O
O
is the origin).
conics
parabola