Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 18"
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− | <math>K(k,0)</math> is the minimum point of the parabola and the parabola intersects the y-axis at the point <math> | + | <math>K(k,0)</math> is the minimum point of the parabola and the parabola intersects the y-axis at the point <math>\Gamma (0,k)</math>. |
− | If the area if the rectangle <math> | + | If the area if the rectangle <math>OAB\Gamma</math> is <math>8</math>, then the equation of the parabola is |
A. <math>y=\frac{1}{2}(x+2)^2</math> | A. <math>y=\frac{1}{2}(x+2)^2</math> |
Revision as of 22:00, 17 October 2007
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
A.
B.
C.
D.
E.
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 , and plugging in point and finding , the answer is .
See also
2006 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 |