1986 AHSME Problems/Problem 18
Contents
[hide]Problem
A plane intersects a right circular cylinder of radius forming an ellipse. If the major axis of the ellipse is longer than the minor axis, the length of the major axis is
Solution
Solution 1
The length of the minor axis is the distance from the opposite points of the cylinder, which is simply , and according to the question, the length of the major axis is simply
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Solution 2
We note that we can draw the minor axis to see that because the minor axis is the minimum distance between two opposite points on the ellipse, we can draw a line through two opposite points of the cylinder, and so the minor axis is . Therefore, our answer is , and so our answer is .
See also
1986 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
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