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JEE Main20231 Feb 2023Evening ShiftMathematicsHyperbolaActual

Let P x 0 , y 0 be the point on the hyperbola 3 x 2 - 4 y 2 = 36 , which is nearest to the line 3 x + 2 y = 1 . Then 2 y 0 - x 0 is equal to :

Options

  1. A- 3
  2. B9
  3. C- 9
  4. D3

Correct answer

C. - 9

Step-by-step solution

Given, Equation of hyperbola, 3 x 2 - 4 y 2 = 36 And nearest line 3 x + 2 y = 1 Now slope of the given line will be, m = - 3 2 Now slope of tangent which will be parallel to given line of hyperbola 3 x 2 - 4 y 2 = 36 is given by, m = 3 sec θ 12 · tan θ Now putting the value of m = - 3 2 we get, ⇒ 3 12 × 1 sin θ = - 3 2 ⇒ sin θ = - 1 3 So, point will be 12 sec θ , 3 tan θ = 12 · 3 2 , - 3 × 1 2 = 6 2 , - 3 2 , Hence, 2 y 0 - x 0 = 2 - 3 2 - 6 2 = - 9

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