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Q.

If a circle passes through the point (1, 2) and cuts the circle x2+y2=4  orthogonally, then the equation of the locus of its centre, is 

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a

2x+4y9=0

b

x2+y23x8y+1=0

c

2x+4y1=0

d

x2+y22x6y7=0

answer is C.

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Detailed Solution

Let the circle be x2+y2+2gx+2fy+c=0. This passes through (1,2)

 5+2g+4f+c=0                     …(i)

The circles x2+y2=4 and x2+y2+2gx+2fy+c=0 cut orthogonally.

 2(g×0+f×0)=c4c=4

Putting c=4 in (i), we get 2g+4f+9=0.

Therefore, the locus of (g,f) is

 2x4y+9=0 or, 2x+4y9=0.

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