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]
Create a free account to view solution
View Solution FreeMore Point Questions
Area of a triangle whose vertices are (a cos θ, b sin θ), (-a sin θ, b cos θ) and (-a cos θ, - ...If the point dividing internally the line segment joining the points (a, b) and (5, 7) in the ratio 2 : 1 be (4, 6), the...The area of an equilateral triangle whose two vertices are (1,0) and (3,0) and third vertex lying in the first quadrant ...If the axes are rotated through an angle of 30o in the anti-clockwise direction, the coordinates of point (4, -2√3...Without changing the direction of coordinates axes, to which point origin should be transferred so that the equation x2 ...