A straight line through the point (2,2) intersects the line √3x+y=0 and √3x-y=0 at the points A and B. What is The equation to the line AB show that the triangle aob is equilateral?

1 Answer
Apr 18, 2018

see explanation.

Explanation:

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I am assuming that #O# is the origin. and I think the question should read as what is the equation of line #AB# so (or such) that the triangle #DeltaAOB# is equilateral.
Given #y=sqrt3x, slope = sqrt3, => alpha=tan^-1sqrt3=60^@#
similarly, as #y=-sqrt3x, => beta=60^@#, as shown in the figure.
#=> angleBOA=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#