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JEE Main202226 Jun 2022Evening ShiftMathematicsHyperbolaActual

The normal to the hyperbola x 2 a 2 - y 2 9 = 1 at the point 8 , 3 3 on it passes through the point

Options

  1. A15 , - 2 3
  2. B9 , 2 3
  3. C- 1 , 9 3
  4. D- 1 , 6 3

Correct answer

C. - 1 , 9 3

Step-by-step solution

Given, hyperbola: x 2 a 2 - y 2 9 = 1 it passes through 8 , 3 3 ∵ 64 a 2 - 27 9 = 1 ⇒ a 2 = 16 Now, equation of normal to hyperbola in point form ∵ 16 x 8 + 9 y 3 3 = 16 + 9 ⇒ 2 x + 3 y = 25 - 1 , 9 3 satisfies the equation.

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