Really? I don't believe it

Geometry Level 3

\(A\) and \(B\) are two points in \(\mathbb{R}^2\). What is the locus of a variable point which moves in such a way that the ratio of its distances from \(A\) and \(B\) is always \(\lambda:1\), where \(\lambda\) is a positive real number not equal to \(1\)?

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