A circle is given by , another circle C touches it externally and also the x-axis, then the locus of its centre is
Let the centre of circle C be (h, k).
Then as this circle touches axis of x its radius = |k| Also it touches the given
circle , centre (0, 1) and radius = 1, externally
Therefore, the distance between centres = sum of radii
Combining the two, the required locus is
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