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Question

If the equation x2+y2+6x2y+(λ2+3λ+12)=0 represent a circle, then

A
λR
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B
λ[1,2]
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C
[2,1]
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D
none of these.
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Solution

The correct option is B λ[1,2]
The general equation of circle is :
x2+y2+2gx+2fy+c=0, where
Center = (g,f) and
Radius = g2+f2c

For the given equation to represent circle, radius must be real
(3)2+(1)2(λ2+3λ+12)R
10(λ2+3λ+12)0
λ2+3λ+20
(λ+2)(λ+1)0
λ[1,2]

Hence, (B) is the correct answer.

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