Question

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?

Answer 1

see explanation.

Explanation:

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`