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Question

The centre of circle passing through (0, 0) and (1, 0) and touching the circle x2+y2=9 is 
(2002)
 


  1. (12,12)

  2. (31,12)

  3. (12,2)

  4. (12,32)


Solution

The correct option is C

(12,2)


Let the required circle be 
x2+y2+2gx+2fy+c=0
Since it passes through (0,0) and (1, 0)
c=0 and g=12

Points (0, 0) and (1, 0) lie inside the circle x2+y2=9, so two circles touch internally 
c1c2=r1r2
g2+f2=3g2+f2g2+f2=32
f2=9414=2          f=±2.
Hence, the centres of required circle are 
(12,2) or 
(12,2)

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