Maxima and MinimaHard
Question
Equation of a straight line passing through (1,4) if the sum of its positive intercepts on the coordinate axis is the smallest is -
Options
A.2x + y - 6 = 0
B.x + 2y - 9 = 0
C.y + 2x + 6 = 0
D.none
Solution
Let the line be (x -1) + λ(y - 4) = 0
x + λy =1 + 4λ
Sum of intercept = 1 + 4λ +
, λ > 0
= 4 λ +
+ 5
⇒ 4λ + 
≥ 4
⇒ 4λ +
+ 5 ≥ 9
equality holds for 4λ =
⇒ λ = 
Required line is x +
= 3
2x + y = 6
x + λy =1 + 4λ
Sum of intercept = 1 + 4λ +
, λ > 0= 4 λ +
+ 5 ⇒ 4λ + ≥ 4⇒ 4λ +
+ 5 ≥ 9equality holds for 4λ =
⇒ λ = Required line is x +
= 32x + y = 6
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