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AP EAMCET201822 Apr 2018Evening ShiftMathematicsHyperbolaActual

If the product of the lengths of the perpendiculars from any point on the hyperbola 16 x^2-25 y^2=400 to its asymptotes is p and the angle between the two asymptotes is , then p 2 =

Options

  1. A400 41
  2. B320 41
  3. C4 5
  4. D25 16

Correct answer

B. 320 41

Step-by-step solution

Equation of given hyperbola is 16 x^2-25 y^2=400 Let a point on hyperbola (i), A(5 , 4 ) , so, lengths of the perpendiculars from point A to the asymptotes is 20 +20 16+25 and 20 -20 16+25 So, P= 400 41 and 2 = 4 5 So, P 2 = 320 41

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