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JEE Main202226 Jul 2022Evening ShiftMathematicsHyperbolaActual

If the line x - 1 = 0 , is a directrix of the hyperbola k x 2 - y 2 = 6 , then the hyperbola passes through the point

Options

  1. A- 2 5 , 6
  2. B- 5 , 3
  3. C5 , - 2
  4. D2 5 , 3 6

Correct answer

C. 5 , - 2

Step-by-step solution

Given equation of hyperbola is x 2 6 k - y 2 6 = 1 Equation of directrix will be x = ± a e , Where e = 1 + b 2 a 2 = 1 + 6 6 k = 1 + k i.e. k ≥ - 1 ⇒ x = ± 6 k 1 + k is the equation of directrix i.e. ± 6 k 1 + k = 1 ∴       k 1 + k 2 = 6 ⇒ k 2 + k - 6 = 0 ⇒   k = 2 as k = - 3 is rejected So equation of hyperbola will be H ≡ x 2 3 - y 2 6 = 1 ∴     5 , - 2 satisfy the given hyperbola

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