Question

Find the combined equation of the pair of lines passing through the origin and making an equilateral triangle with the line y = 3.

Answer 1

Let OA and OB be the lines through the origin making.an angle of 60° with the line y = 3.

∴ OA and OB make an angle of 60° and 120° with the positive direction of X-axis.

∴ slope of OA = tan60° = √3

∴ equation of the line OA is

y = √3x, i.e. √3x – y = 0

Slope of OB = tan 120° = tan (180° – 60°) = -tan 60°= - √3

∴ equation of the line OB is

y = –√3 x, i.e. √3 x + y = 0

i.e. 3x² – y = 0