2006 Cyprus MO/Lyceum/Problem 18
Revision as of 13:39, 26 April 2008 by I like pie (talk | contribs) (Standardized answer choices; minor edits to solution)
Problem
is the minimum point of the parabola and the parabola intersects the y-axis at the point
.
If the area if the rectangle
is
, then the equation of the parabola is
Solution
Since the parabola is symmetric about the line ,
has coordinates
. The area of the rectangle is
, so the vertex is at
.
Thus, the equation of the parabola is . Plugging in point
, we find
, and the answer is
.
See also
2006 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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