Maharashtra State BoardHSC Arts 12th Board Exam
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Find ‘k’, if the equation kxy + 10x + 6y + 4 = 0 represents a pair of straight lines. - Mathematics and Statistics

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Find ‘k’, if the equation kxy + 10x + 6y + 4 = 0 represents a pair of straight lines.

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Solution

Given equation is kxy + 10x + 6y + 4 = 0

Comparing with ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, we get

a = 0, h = k/2 , b = 0, g = 5, f = 3, c = 4

Since the given equation represents a pair of lines.
abc + 2fgh - af2 - bg2 -ch2 = 0

(0)(0)(4)+2(3)(5)(k/2)-(0)(3)^2-(0)(5)^2-4(k/2)^2=0

15k - k2 = 0
- k2 + 15k = 0
- k(k - 15) = 0
 k = 0 or k = 15
If k = 0, then the equation becomes
10x + 6y + 4 = 0 which does not represents a pair of lines.
 k ≠ 0
Hence, k = 15.

Concept: Acute Angle Between the Lines
  Is there an error in this question or solution?

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