2004 AMC 12B Problems/Problem 18
Problem
Points and
are on the parabola
, and the origin is the midpoint of
. What is the length of
?
Solution
Let the coordinates of be
. As
lies on the parabola, we have
.
As the origin is the midpoint of
, the coordinates of
are
.
We need to choose
so that
will lie on the parabola as well. In other words, we need
.
Substituting for , we get:
.
This simplifies to , which solves to
. Both roots lead to the same pair of points:
and
. Their distance is
.
See Also
2004 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 17 |
Followed by Problem 19 |
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All AMC 12 Problems and Solutions |