The equation of a circle of radius 1 touching the circles x^2+y^2-2|x|=0 is

JEE Advanced Mathematics question

The equation of a circle of radius 1 touching the circles is

(A)
(B)Correct
(C)Correct
(D)

Answer: (B),(C)

Solution

is the pair of circles ( and ), centres , radius 1, touching at . A circle of radius 1 touching a circle of radius 1 (and not coinciding with it) must touch it externally, so its centre is at distance 2 from both and : it

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Question ID VK-108973