ParabolaHard
Question
If the focus of the parabola (y - λ)2 = 4(x - λ) always lies between the lines 2x + y = 1 and 2x + y = 3 then the sum of all integral values of λ is -
Options
A.0
B.1
C.2
D.infinite
Solution
Focus of parabola is (λ + 1, λ)
∴ (2(λ + 1) + λ - 1). (λ + 1 + 2λ - 3) < 0
⇒ (3λ + 1)(3λ - 1) < 0 ⇒
∴ Integral value of λ is 0.
∴ (2(λ + 1) + λ - 1). (λ + 1 + 2λ - 3) < 0
⇒ (3λ + 1)(3λ - 1) < 0 ⇒
∴ Integral value of λ is 0.
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