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If the equation x^(2)+y^(2)+6x-2y+(lam...

If the equation ` x^(2)+y^(2)+6x-2y+(lambda^(2)+3lambda+12)=0` represent a circle. Then

A

`lambda in R`

B

`lambda in [1, 2]`

C

`[-2, -1]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
The given equation will represent a circle if
`9+1-(lambda^(2)+3lambda+12)ge0 " "[:' g^(2)+f^(2)-cge0]`
`rArr -lambda^(2)-3lambda-2ge0`
`rArr lambda^(2)+3lambda+2 le 0 rArr (lambda+1)(lambda+2) le 0 rArr lambda in [-2, -1]`
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OBJECTIVE RD SHARMA-CIRCLES-Section I - Solved Mcqs
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  2. The number of integral values of lambda for which the equation x^(2)+y...

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  3. If the equation x^(2)+y^(2)+6x-2y+(lambda^(2)+3lambda+12)=0 represen...

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  6. Prove that the locus of a point which moves such that the sum of th...

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  11. If the base of a triangle and the ratio of the lengths of the other tw...

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  12. Two conics a1x^2+2h1xy + b1y^2 = c1, a2x^2 + 2h2xy+b2y^2 = c2 interse...

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  13. The number of points with integral coordinates that are interior to t...

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  14. Find the equation of the circle which is touched by y=x , has its cent...

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  15. The locus of the centre of the circle which cuts the circle x^2 + y^2 ...

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  16. From the point A(0,3) on the circle x^2 +4x + (y-3)^2 = 0 a chord AB ...

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  17. Two vertices of an equilateral triangle are (-1,0) and (1, 0), and its...

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  18. The geometric mean of the minimum and maximum values of the distance...

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  19. A circle passes through a fixed point A and cuts two perpendicular str...

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  20. The equation of the circumcircle of the triangle formed by the lines w...

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