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Question

The locus of the centres of all circle passing through (1,2) and cutting x2+y2=16 orthogonally is

A
4x2y+21=0
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B
x+2y+11=0
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C
2x+4y21=0
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D
2xy+11=0
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Solution

The correct option is C 2x+4y21=0
Let (x1,y1) be the centre of circle
Also Equation of circle be
x2+y2+2gx+2fy+c=0
Substituting (1,2)
12+22+2g(1)+2f(2)+c=0
5+c=2(g+2f)
g+2f=(5+c2)
2gg1+2ff1=c+c1 orthogonality condn
0+0=16+c(g1=f1=0)
c=16
g+2f=(5+162)
g+2f=212
Now x1=gy1=f
x12y1=212
2x14y1=21
2x1+4y1+21=0
Locus :- 2x+4y21=0

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