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Question

The straight line y=2x+λ does not meet the parabola y2=2x, if


A

λ<14

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B

λ>14

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C

λ=4

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D

λ=1

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Solution

The correct option is B

λ>14


Line y=2x+λ .......(i)Parabola y2=2x ......(ii)Solving (i) & (ii) we get, (2x+λ)2=2x4x2+4xλ+λ2=2x4x2+2x(2λ1)+λ2=0
Line does not meet the parabola
D<04(2λ1)24(4)(λ2)<04[4λ2+14λ4λ2]<014λ<0λ>14


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