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Three Dimensional Geometry
Question
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The curve y = (λ + 1)x2 + 2 intersects the curve y = λx + 3 in exactly one point, if λ equals -

  • {–2, 2}

  • {1}

  • {-2}

  • {2}

Answer

C.

{-2}

for point of intersection at exactly one point
λx + 3 = (λ + 1)x2 + 2
(λ + 1)x2 – λx – 1 = 0
Δ = 0
λ2 + 4(λ + 1) = 0
λ2 + 4λ + 4 = 0
(λ + 2)2 = 0 λ = – 2

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