1985 AHSME Problems/Problem 10
Problem
An arbitrary circle can intersect the graph of in
Solution
Consider a circle whose center lies on the positive -axis and which passes through the origin. As the radius of this circle becomes arbitrarily large, its curvature near the -axis becomes almost flat, and so it can intersect the curve arbitrarily many times (since the -axis itself intersects the curve infinitely many times). Hence, in particular, we can choose a radius sufficiently large that the circle intersects the curve at .
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
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Followed by Problem 11 | |
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