Maharashtra State BoardHSC Arts 12th Board Exam
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If 2x + Y = 0 is One of the Lines Represented by 3x2 + Kxy + 2y2 = 0, Then the Value of K is - Mathematics and Statistics

MCQ

If 2x + y = 0 is one of the lines represented by 3x2 + kxy + 2y2 = 0, then the value of k is

Options

  • `1/2`

  • `11/2`

  • `5/2`

  • `(-11)/2`

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Solution

Auxiliary equation of the given equation is 2m2 + km + 3 = 0.

Slope of the line 2x + y = 0 is m = − 2.

∴ m = −2 is a root of the auxiliary equation 2m2 + km + 3 = 0

∴ 2(−2)2 − 2k + 3 = 0

∴ 8 − 2k + 3 = 0

∴ k = `11/2`

Concept: Pair of Straight Lines - Pair of Lines Passing Through Origin - Combined Equation
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