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Question
Find the joint equation of the line passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18
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Solution
Let L1 and L2 be the lines passing through the origin and perpendicular to the lines x + 2y = 19 and 3x + y = 18 respectively.
Slopes of the lines x + 2y = 19 and 3x + y = 18 are `-1/2` and `- 3/1` = -3 respectively.
∴ slopes of the lines L1 and L2 are 2 and `1/3` respectively.
Since the lines L1 and L2 pass through the origin, their equations are
y = 2x and y = `1/3`x
i.e. 2x - y = 0 and x - 3y = 0
∴ their combined equation is
(2x - y)(x - 3y) = 0
∴ 2x2 - 6xy - xy + 3y2 = 0
∴ 2x2 - 7xy + 3y2 = 0
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