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Question

If one of the diameters of the circle x2+y22x6y+6=0 is a chord to the circle with centre (2,1), then the equation of the circle is

A
x2+y24x2y+2=0
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B
x2+y24x2y2=0
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C
x2+y24x2y4=0
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D
x2+y24x2y+4=0
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Solution

The correct option is C x2+y24x2y4=0
According to the given question


The given circle is
x2+y22x6y+6=0
C=(g,f)=(1,3)
r=g2+f2c=1+96=2

Let AB be one of its diameter which is the chord of other circle with center C1(2,1), so in C1CB, we have
(C1B)2=(CC1)2+(CB)2r2=[(21)2+(13)2]+22
r=3

Hence, the equation of the other circle is
(x2)2+(y1)2=32x2+y24x2y4=0

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