Difference between revisions of "2015 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 5"
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Let <math>A</math> and <math>B</math> be two points in the plane. Describe the set <math>S</math> of all points in the plane such | Let <math>A</math> and <math>B</math> be two points in the plane. Describe the set <math>S</math> of all points in the plane such | ||
− | that for any point <math>P</math> in <math>S</math> we have <cmath>|PA| = 3|PB|</cmath> | + | that for any point <math>P</math> in <math>S</math> we have <cmath>|PA| = 3|PB| \text{.}</cmath> |
== Solution== | == Solution== |
Latest revision as of 13:29, 21 January 2024
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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