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Question
Find the joint equation of the line passing through the origin having slopes 2 and 3.
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Solution
We know that the equation of the line passing through the origin and having slope m is y = mx.
Equations of the lines passing through the origin and having slopes 2 and 3 are y = 2x and y = 3x, respectively.
i.e., their equations are 2x − y = 0 and 3x − y = 0 respectively.
∴ Their joint equation is
(2x − y)(3x − y) = 0
∴ 6x2 − 2xy − 3xy + y2 = 0
∴ 6x2 − 5xy + y2 = 0
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