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Question

The coordinates of the centre of a circle, whose radius is 2 units and which touches the line pair x2y22x+1=0, are


A
(4,0)
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B
(1+22,0)
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C
(4,1)
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D
(1,22)
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Solution

The correct option is D (1,22)
Line pair is (x1)2y2=0,
i.e., x+y1=0, xy1=0


If the centre is on the x-axis,
let the centre be (α,0).
Then its distance from x+y1=0 is
α12=2 (radius)
i.e., α=1±22
Centre may be (1+22,0),(122,0)

If the centre is on the line x=1,
let the centre be (1,β).
Then 1+β12=2
β=±22
Centre may be (1,22),(1,22)

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