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Question

The circle x2+y2=4 cuts the circle x2+y2−2x−4=0 at the points A and B. If the circle x2+y2−4x−k=0 passes through A and B then the value of k is

A
4
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B
0
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C
8
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D
4
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Solution

The correct option is C 4
Centre of the circle x2+y22x4=0 is (1,0)

And the centre of the circle x2+y2=4 is (0,0) .

Centre of the circle x2+y24xk=0 is (2,0)

To find the intersection points of x2+y22x4=0 and x2+y2=4

Put x2+y2=4 in the equation of the circle x2+y22x4=0, we get

42x4=0x=0y=±2

x2+y22x4=0 and x2+y2=4 intersect at (0,2) and (0,2)

If the circle x2+y24xk=0 passes through (0,2) and (0,2), then the distance between the centre (2,0) and the above points is equal to the radius of the circle.

4+k=22+224+k=8k=4

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