2007 Cyprus MO/Lyceum/Problem 23
Problem
In the figure above the right section of a parabolic tunnel is presented. Its maximum height is and its maximum width is . If M is the midpoint of , then the height of the tunnel at the point is
Solution
Since it is a parabolic tunnel, the equation of the tunnel is a quadratic. We have three points: (0,8), (10,0), and (-10,0). Since we have both of the roots, we multiply . But we also have , so . Thus the equation of the parabola is . Now the height of the tunnel at M is the value of the y coordinate when , or .
See also
2007 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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