the larger of the two angles made with the x axis of a straight line drawn through [1,2]so that it intersect x+y=4 at a distance root6/3
from [1,2] is

Question

the larger of the two angles made with the x axis of a straight line drawn through [1,2]so that it intersect x+y=4 at a distance root6/3 from [1,2] is

Badiuddin askIITians.ismu Expert · Answer

Dear jauneet singh

here distance form of a line is very helpful

equation of line

(x-1)/ =(y-2)/sinΘ =√6 /3

so x=1+√6 cosΘ /3

and y =2 +√6 sinΘ /3

These point lie on the line x+y =4

so 1+√6 cosΘ /3 +2 +√6 sinΘ /3 =4

or √6 /3 (cosΘ +sinΘ) =1

or 1/√2 (cosΘ +sinΘ) =√3 /2

or sin(Θ+45) =sin 60 or sin 120

for larger angle

sin(Θ+45) =sin 120

Θ=75

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Badiuddin

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the larger of the two angles made with the x axis of a straight line drawn through [1,2]so that it intersect x+y=4 at a distance root6/3 from [1,2] is

the larger of the two angles made with the x axis of a straight line drawn through [1,2]so that it intersect x+y=4 at a distance root6/3
from [1,2] is

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