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Most Important Selected Qs for JEE AdvancedMathematicsStraight Lines

If a is an integer and m₁, m₂, m₃ are the slopes of all three straight lines represented by equation y^3+(2 a+5) x y^2-6 x^2 y-2 a x^3=0 which are also integers, then which of the following can holds good?

Options

  1. Aa+ _ i=1 ^3 m_i=-1
  2. Ba+ _ i=1 ^3 m_i=-5
  3. Ca+ _ i=1 ^3 m_i=0
  4. Da+ _ i=1 ^3 m_i=32

Correct answer

C. a+ _ i=1 ^3 m_i=0

Step-by-step solution

aligned & m₁+m₂+m₃=-(2 a+5) & m₁ m₂+m₂ m₃+m₃ m₁=-6 & m₁ m₂ m₃=2 a & For (A) aligned aligned & a+ _ i=1 ^3 m_i=-1 & a-2 a-5=-1 a=-4 m₁ m₂ m₃=-8 & m₁=1, m₂=-2, m₃=4 m₁ m₂ m₃=-8 & for (B) & a-2 a-5=-5 a=0 m₁ m₂ m₃=0 & m₁=1, m₂=0, m₃=-6 & . a+ _ i=1 ^3 m_i=0+0=0 ( C is correct ) aligned for (D) a+2 a=32 not possible Hence (D) is incorrect.

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