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The larger of the two angles made with x-axis of a straight line drawn through (1,2) so that it intersects x+y= 4 at a distance (√6 ) / 3 from (1,2) is : -
suppose a line passing through (1,2)makes an angle A with x-axis.then its eqn isx-1/cosA =y-2/sinAthe coordinates of pt on line at a distance√6/3=√2/3 from (1,2)are given byx-1/cosA =y-2/sinA=√2/3 or ,(1+√2/3*cosA ,2+√2/3*sinA)this pt lies on x+y =4cosA+sinA=√3/2sin(A+/4)=√3/2A+/4=/3,2/3A=/12,5/12A=15 or 75
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