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प्रश्न
Find the value of k, if the following equations represent a pair of line:
3x2 + 10xy + 3y2 + 16y + k = 0
उत्तर
Comparing the given equation with
ax2 + 2hxy + by2 + 2gx + 2fy + c = 0
we get, a = 3, h = 5, b = 3, g = 0, f = 8, c = k.
Now, the given equation represents a pair of lines.
∴ abc + 2fgh - af2 - bg2 - ch2 = 0
∴ (3)(3)(k) + 2(8)(0)(5) - 3(8)2 - 3(0)2 - k(5)2 = 0
∴ 9k + 0 - 192 - 0 - 25k = 0
∴ - 16k - 192 = 0
∴ - 16k = 192
∴ k = - 12
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