CircleMedium
Question
Equation (2 + λ)x2 - 2λxy + (λ - λ)y2 - 4x - 2 = 0 represents a hyperbola if -
Options
A.λ = 4
B.λ = 1
C.λ = 4/3
D.λ = - 1
Solution
Given equation will represent hyperbola if
λ2 > (λ + 2) (λ - 1) [ h2 > ab]
⇒ λ < 2
Also ᐃ ≠ 0
⇒ -2 (λ2 + λ - 2) - 4 (λ - 1) + 2λ2 ≠ 0
⇒ λ ≠
λ2 > (λ + 2) (λ - 1) [ h2 > ab]
⇒ λ < 2
Also ᐃ ≠ 0
⇒ -2 (λ2 + λ - 2) - 4 (λ - 1) + 2λ2 ≠ 0
⇒ λ ≠
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