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Question
Find the separate equations of the lines represented by the equation 3x2 – 10xy – 8y2 = 0.
Solution
Given pairs of lines 3x2 – 10xy – 8y2 = 0
⇒ 3x2 – 12xy + 2xy – 8y2 = 0
⇒ 3x(x – 4y) + 2y(x – 4y) = 0
⇒ (x – 4y)(3x + 2y) = 0
Separated equations are:
3x + 2y = 0 and x – 4y = 0
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