PointHard
Question
A triangle is formed by the lines 2x - 3y - 6 = 0 ; 3x - y + 3 = 0 and 3x + 4y - 12 = 0. If the points P(α, 0) and Q (0, β) always lie on or inside the ᐃABC, then range of α & β -
Options
A.α ∈[-1, 2] & β ∈ [-2, 3]
B.α ∈[-1, 3] & β ∈ [-2, 4]
C.α ∈[-2, 4] & β ∈ [-3, 4]
D.α ∈[-1, 3] & β ∈ [-2, 3]
Solution
(i) 4β - 12 < 0 ⇒ β < 3
3α - 12 < 0 ⇒ α < 4
(ii) -β + 3 > 0 ⇒ β < 3
3α + 3 > 0 ⇒ α > -1
(iii) 2α - 6 < 0 ⇒ α < 3
-3β - 6 < 0 ⇒ β < -2
From cases (i), (ii) & (iii)
α ∈ [1-, 3] & β ∈ [-2, 3]
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