If the pair of straight lines ax 2 + 2hxy – ay 2 = 0 and bx 2 + 2gxy – by 2 =0 be such that each bisect the angle between the other , then hg + ab = 0 ah + bg = 0 h 2 – ab = 0 ag + bh = 0

Question

Latika Leekha · Answer

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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If the pair of straight lines ax 2 + 2hxy – ay 2 = 0 and bx 2 + 2gxy – by 2 =0 be such that each bisect the angle between the other , then hg + ab = 0 ah + bg = 0 h 2 – ab = 0 ag + bh = 0

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

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If the pair of straight lines ax 2 + 2hxy – ay 2 = 0 and bx 2 + 2gxy – by 2 =0 be such that each bisect the angle between the other , then hg + ab = 0 ah + bg = 0 h 2 – ab = 0 ag + bh = 0

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

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