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 : -

Question

Arun · Answer

suppose a line passing through (1,2)makes an angle A with x-axis.then its eqn is
x-1/cosA =y-2/sinA
the coordinates of pt on line at a distance
√6/3=√2/3 from (1,2)are given by
x-1/cosA =y-2/sinA=√2/3 or ,(1+√2/3*cosA ,2+
√2/3*sinA)
this pt lies on x+y =4
cosA+sinA=√3/2
sin(A+ $\huge \pi$ /4)=√3/2
A+ $\huge \pi$ /4= $\huge \pi$ /3,2 $\huge \pi$ /3
A= $\huge \pi$ /12,5 $\huge \pi$ /12
A=15 or 75

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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 : -

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 : -

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