2015 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 5
Problem
Let and be two points in the plane. Describe the set of all points in the plane such that for any point in we have
Solution
WLOG, let , and . That means that we have that for any point , . Conic sections written in the form are circles if and only if , which is true in our equation. Therefore, S is a circle. ~Puck_0
See also
2015 UNM-PNM Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNM-PNM Problems and Solutions |
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