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Question
Find the separate equations of the lines given by x2 + 2xy tan α − y2 = 0
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Solution
The given equation of the lines is x2 + 2xy tan α − y2 = 0
The auxiliary equation of the given combined equation of the lines is m2 − 2m tan α − 1 = 0
∴ m = `(2 tan alpha ± sqrt(4tan^2 alpha + 4))/2`
= `(2 tan alpha ± 2sqrt(tan^2 alpha + 1))/2`
∴ m = tan α ± sec α
∴ m1 = tan α + sec α and m2 = tan α − sec α
∴ The separate equations of lines are
y = (tan α + sec α)x and y = (tan α − sec α)x
∴ (sec a + tan a)x − y = 0 and (sec a − tan a)x + y = 0
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