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3
2019 T3: Equidistant Points on a Parabola
2019 T3: Equidistant Points on a Parabola
Source:
January 27, 2019
2019
team
conics
parabola
Problem Statement
Points
A
(
0
,
0
)
A(0,0)
A
(
0
,
0
)
and
B
(
1
,
1
)
B(1,1)
B
(
1
,
1
)
are located on the parabola
y
=
x
2
y=x^2
y
=
x
2
. A third point
C
C
C
is positioned on this parabola between
A
A
A
and
B
B
B
such that
A
C
=
C
B
=
r
AC=CB=r
A
C
=
CB
=
r
. What is
r
2
r^2
r
2
?
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