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प्रश्न
Find k, the slope of one of the lines given by kx2 + 4xy – y2 = 0 exceeds the slope of the other by 8.
उत्तर
Comparing the equation kx2 + 4xy – y2 = 0 with ax2 + 2hxy – by2 = 0, we get, a = k, 2h = 4, b = –1.
Let m1 and m2 be the slopes of the lines represented by kx2 + 4xy – y2 = 0
∴ m1 + m2 = `(-2h)/b = -4/(-1)` = 4 ...(1)
and m1m2 = `a/b = k/(-1)` = –k ...(2)
We are given that m2 = m1 + 8
4 – m1 = m1 + 8 ...[By (1)]
∴ 2m1 = –4
∴ m1 = –2 ...(3)
Also, m1(m1 + 8) = –k ...[By (2)]
(–2)(–2 + 8) = –k ...[By (3)]
∴ (–2)(6) = –k
∴ –12 = –k
∴ k = 12
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