Locus of circle's centre

Geometry Level 3

Which of the following can represent the equation of a locus of a centre of a circle touching both another circle and a straight line which in turn do not intersect?

eg.

Let \(C_1\) be the required circle and \(C_2\) given circle and \(L_1\) be the given line then:

  1. \(C_1\) touches \(L_1\) and \(C_2\).

  2. \(C_2\) does not touch \(L_1\).

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