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AP EAMCET202023 Sep 2020Morning ShiftMathematicsHyperbolaActual

The equation of the asymptotes of the hyperbola 2 x 2 + 5 x y + 2 y 2 - 11 x - 7 y - 4 = 0 is

Options

  1. A2 x 2 + 5 x y + 2 y 2 - 11 x - 7 y - 9 = 0
  2. B2 x 2 + 5 x y + 2 y 2 - 11 x - 7 y + 5 = 0
  3. C2 x 2 + 5 x y + 2 y 2 - 11 x - 7 y + 4 = 0
  4. D2 x 2 + 5 x y + 2 y 2 - 11 x - 7 y + 9 = 0

Correct answer

B. 2 x 2 + 5 x y + 2 y 2 - 11 x - 7 y + 5 = 0

Step-by-step solution

Equation of the asymptotes of the given hyperbola is 2 x 2 + 5 x y + 2 y 2 - 11 x - 7 y + λ = 0 This equation should represent line pair So, a b c + 2 f g h - a f 2 - b g 2 - c h 2 = 0 a = 2 b = 2 c = λ h = 5 2 g = - 11 2 f = - 7 2 4 λ + 385 4 - 2 × 49 4 - 2 × | 2 | 4 - λ × 25 4 = 0 ⇒ - 9 λ + 45 = 0 ⇒ λ = 5 2 x 2 + 5 x y + 2 y 2 - 11 x - 7 y + 5 = 0

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