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If the equation
$x^{2} + y^{2} + 6 x - 2 y + (λ^{2} + 3 λ + 12) = 0$ represents a circle, then

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λ∈R

λ∈[1,2]

[−2,−1]

none of these

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detailed solution

Correct option is C

The given equation will represent a circle if9+1−λ2+3λ+12≥0 ∵g2+f2−c≥0⇒ −λ2−3λ−2≥0⇒ λ2+3λ+2≤0⇒(λ+1)(λ+2)≤0⇒λ∈[−2,−1]

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If the equationx2+y2+6x−2y+λ2+3λ+12=0 represents a circle, then

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If the equation
$x^{2} + y^{2} + 6 x - 2 y + (λ^{2} + 3 λ + 12) = 0$ represents a circle, then