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Question
Find the combined equation of lines passing through the origin and each of which making an angle of 60° with the Y-axis.
Solution
Let OA and OB be the lines through the origin making an angle of 60° with the Y-axis.
Then OA and OB make an angle of 30° and 150° with the positive direction of X-axis.
∴ slope of OA = tan 30° = `1/sqrt3`
∴ equation of the line OA is
y = `1/sqrt3` x i.e. `"x" - sqrt3"y" = 0`
Slope of OB = tan 150° = tan (180° - 30°)
= - tan 30° = `- 1/sqrt3`
∴ equation of the line OB is
y = `- 1/sqrt3 "x"` i.e. x + `sqrt3`y = 0
∴ required combined equation is
`("x" - sqrt3"y")("x" + sqrt3"y") = 0`
i.e. x2 - 3y2 = 0
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