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Question

Equation of the circle which is such that the lengths of the tangents to it from the points (1,0),(2,0) and (3,2) and 1,7,2 respectively is

A
6(x2+y2)28x5y+28=0
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B
9(x2+y2)28x5y+28=0
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C
3(x2+y2)28x5y+28=0
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D
x2+y228x5y+28=0
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Solution

The correct option is B 6(x2+y2)28x5y+28=0
Circle x2+y2+2gx+2fy+c=0
Length of tangent =5
Lengths given are 1,7,2
1+0+2g+0+c=1
2g+c+1=1
2g+c+1=1
c=2g(1)
4+0+4g+c=7
4g+4+c=7
4g+c=3(2)
g+4+6g+4f+c=2
6g+4f+c+13=2
6g+4f+c=11(3)
Putting (1) in (2)
4g2g=3
g=32
c=3
Putting in (3)
6(32)+4f3=11
g+4f3=11
4f+6=11
f=174
Circle x2+y2+3x172y3=0

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