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If the pair of straight lines ax2 + 2hxy – ay2 = 0 and bx2 + 2gxy – by2 =0 be such that each bisectthe angle between the other , thenhg + ab = 0ah + bg = 0h2 – ab = 0ag + bh = 0

Kartikey Sharma , 9 Years ago
Grade 12th pass
anser 1 Answers
Latika Leekha

Last Activity: 9 Years ago

Hello student,
The equation of the bisectors of angles between the lines ax2 + 2hxy - ay2 = 0 is
(x2-y2)/(a-(-a)) = xy/h
or hx2 - 2axy – hy2 = 0 ….…. (1)
Also, bx2 + 2gxy – by2 = 0 …. (2)
Therefore, from (1) and (2), by comparing the coefficients, we get
h/b = -2a/2g
So, hg = -ab or hg + ab = 0.

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