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Show that the equation to the pair of bisectors of angles between the pair of lines ax^2 + 2hxy + by^2 = 0 is h(x^2 – y^2) = (a – b)xy.

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Show that the equation to the pair of bisectors of angles between the pair of lines ax2 + 2hxy + by2 = 0 is h(x2 – y2) = (a – b)xy.

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Let ax2 + 2hxy + by2 = 0 represent the lines l1x + m1y = 0 → (1), l2x + m2y = 0 → (2) 

Thus (l1x + m1y) (l2x + m2y) ≡ ax2 + 2hxy + by2 

⇒ l1l2 = a, m1 m2 = b, l1m2 + l2m1 = 2h 

The equations to the bisectors of angles between (1) and (2) are

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