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The line K + 1 2 x + Ky - 2 K 2 - 2 = 0 passes through the point m , n for all real values of K , then

Options

  1. Am + n = 2
  2. Bm - n = 6
  3. Cm n = 2
  4. Dm n = 1 2

Correct answer

B. m - n = 6

Step-by-step solution

K + 1 2 m + K n - 2 K 2 - 2 = 0, ∀ K ∈ R ⇒ m - 2 K 2 + 2 m + n K + m - 2 = 0, ∀ K ∈ R ⇒ m - 2 = 0 & 2 m + n = 0 ⇒ m = 2 & n = - 4 ⇒ m + n = - 2 , m - n = 6 , m n = - 1 2

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