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Question

The straight line x+y1=0 meets the circle x2+y26x8y=0 at A and B. Then the equation of the circle of which AB is a diameter is

A
x2+y22y6=0
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B
x2+y2+2y6=0
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C
2(x2+y2)+2y6=0
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D
3(x2+y2)+2y6=0
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Solution

The correct option is D x2+y22y6=0
x2+y26x8y+λ(x+y1)=0
Centre =(3λ2,4λ2) lies on x+y1=0
So, the centre satisfy the equation x+y1=0
(3λ2)+(4λ2)1=0
6λ=0λ=6
Hence, required equation is given by
x2+y26x8y+6x+6y6=0
x2+y22y6=0

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