1965 AHSME Problems/Problem 13
Problem
Let be the number of number-pairs which satisfy and . Then is:
Solution
For an ordered pair to satisfy the restrictions, the point must lie on the graph of the line (shown in blue in the diagram) and on the closed disk given by (whose boundary is red in the diagram). Because the -intercept of the line, , is within the disk (and not on the boundary of the disk), the line cannot be tangent to the disk, and so the disk must contain infinitely many of the points on the line. Thus, our answer is
See Also
1965 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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