Question #1a839

1 Answer
Jan 13, 2018

Equation of line #AB# is #y=2#

Explanation:

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#O(0,0)# is the intersection point of the two given lines #sqrt3x+y=0, and sqrt3x-y=0#,
Given #y=sqrt3x, slope = sqrt3, => alpha=tan^-1sqrt3=60^@#
similarly, given #y=-sqrt3x, => beta=60^@#, as shown in the figure.
#=> angleAOB=180-60-60=60^@#
For #DeltaOAB# to be equilateral, line #AB# has to be parallel to the x-axis.
Hence, equation of line #AB# that passes through #P(2,2)# and is parallel to the x-axis is : #y=2#