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प्रश्न
Find k, if the slopes of lines given by kx2 + 5xy + y2 = 0 differ by 1.
उत्तर
Comparing the equation kx2 + 5xy + y2 = 0 with ax2 + 2hxy + by2 = 0, we get,
a = k, 2h = 5 i.e. h = `5/2`
m1 + m2 = `(-"2h")/"b" = -5/1 = -5`
and m1m2 = `"a"/"b" = "k"/1 = "k"`
the slope of the line differ by (m1 - m2) = 1 ....(1)
∴ (m1 - m2)2 = (m1 + m2)2 - 4m1m2
(m1 - m2)2 = (- 5)2 - 4(k)
(m1 - m2)2 = 25 - 4k
1 = 25 - 4k .....[By(1)]
4k = 24
k = 6
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