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Question
Find the joint equation of the line passing through the origin and having inclinations 60° and 120°.
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Solution
Slope of the line having inclination θ is tan θ.
Inclinations of the given lines are 60° and 120°
∴ their slopes are m1 = tan 60° = `sqrt3` and
m2 = tan 120° = tan (180° - 60°)
= - tan 60° = - `sqrt 3`.
Since the lines pass through the origin, their equations are
y = `sqrt3"x"` and y = `- sqrt3"x"`
i.e. `sqrt3"x - y" = 0` and `sqrt3"x + y" = 0`
∴ the joint equation of these lines is
`(sqrt3"x - y")(sqrt3"x + y") = 0`
∴ 3x2 - y2 = 0
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