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Question

Two lines passing through the point (2,3) intersects each other at an angle of 60. If slope of one line is 2 , find equation of the other line.

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Solution

tanθ=m1m21+m1m2
3=|2m|1+2m3+23m=12ml
(23+1)m=23 or (231)m=2+3
m=2323+1 or 2+3231
equation of line =(y3)=2±3231(x2) ;
(231)(y3)=(2±3)(x2)
23yy63+3=2x4+3x23 or 23y63+y3=2x43x+23
(231)(3+2)x=7+43 or (23+1)y+(32)x=1+83

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