MathDB
Choose the Figure in Complex Plane

Source: 1993 National High School Mathematics League, Exam One, Problem 6

February 27, 2020

Problem Statement

m,nm,n are non-zero-real numbers, z∈Cz\in\mathbb{C}. Then, the figure of equations ∣z+ni∣+∣z−mi∣=n|z+n\text{i}|+|z-m\text{i}|=n and ∣z+ni∣−∣z−mi∣=−m|z+n\text{i}|-|z-m\text{i}|=-m in complex plane is (F1,F2F_1,F_2 are focal points) https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvMS84L2RkYWZjM2JmNTc0N2RmYjJlMGUwMGFmMWRkY2RkZTA4NTljZTUwLnBuZw==&rn=MTI0NTI0NTQucG5n
Back to ProblemsView on AoPS