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Question

The number of integral values of λ for which the equation x2+y2+λx+(1λ)y+5=0 is the equation of a circle whose radius cannot exceed 5, is


A

14

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B

18

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C

16

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D

None of these

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Solution

The correct option is C

16


According to the question :
(λ2)2+(λ12)255

(λ2)2+(λ12)230

λ2+(λ1)2120

2λ22λ1190

Using quadratic formula:

λ=2±224(2)(119)2(2)

λ=2±9564

λ=1±2392

λ=7.23,85237.23λ8.23

λ=7,6,5,4,3,2,1,0,1,2,3,4,5,6,7,8(If λεz)

Thus, the number of integral values of λ is 16.


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