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Geometry Level 3

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

Circle Hyperbola Catenary Nondegenerate parabola None of the rest Non-circle ellipse Straight line Finite set of points

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