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Question

If the line 3x+2λy+12=0 is a diameter of the circle x2+y24x+6y+12=0, then the value of λ is

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Solution

Given line is
3x+2λy+12=0
Equation of the circle is
x2+y24x+6y+12=0,
Centre of the circle is
C=(g,f)=(2,3)
Centre should lie on the equation of diameter, so
3(2)+2λ(3)+12=0λ=3

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