Question

Question #1a839

Answer 1

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

Explanation:

`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`