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For the hyperbola x 2 a 2 - y 2 b 2 = 1 , distance between the foci is 10 units. From the point 2 , 3 , perpendicular tangents are drawn to the hyperbola, then the value of b a is

Options

  1. A0 . 25
  2. B5
  3. C0 . 75
  4. D1

Correct answer

C. 0 . 75

Step-by-step solution

Let, e be the eccentricity of the hyperbola Now, 2 a e = 10 ⇒ a 2 e 2 = 25 ⇒ a 2 + b 2 = 25 Also 2 , 3 lies on the director circle x 2 + y 2 = a 2 - b 2 ⇒ 7 = a 2 - b 2 ⇒ a 2 = 16 ,   b 2 = 9 ⇒ b a = 3 4 = 0 . 75

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