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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 , thenhg + ab = 0 ah + bg = 0h2 – ab = 0 ag + bh = 0
Hello student,The equation of the bisectors of angles between the lines ax2 + 2hxy - ay2 = 0 is(x2-y2)/(a-(-a)) = xy/hor hx2 - 2axy – hy2 = 0 ….…. (1)Also, bx2 + 2gxy – by2 = 0 …. (2)Therefore, from (1) and (2), by comparing the coefficients, we geth/b = -2a/2gSo, hg = -ab or hg + ab = 0.
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