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Paragraph: An asymptote to a curve is a straight line which tends to be become tangent when point of contact approaches to infinity. Let the equation of hyperbola is S =0 , then the equation of its asymptotes is S + =0 , which will be pair of lines. On the basis of above information answer the following : Question: The product of perpendiculars from any point on the hyperbola x^2 16 - y^2 25 =1 to its asymptotes is e

Options

  1. A20 9
  2. B400 9
  3. C20 41
  4. D400 41

Correct answer

D. 400 41

Step-by-step solution

Asymptotes of the hyperbola x^2 16 - y^2 25 =1 will be x^2 16 - y^2 25 =0 ( x 4 + y 5 ) ( x 4 - y 5 )=0 Now any point on the hyperbola will be (4 , 5 ) length of the perpendicular from this point to the asymptotes will be aligned p ₁ & = (20 +20 ) 41 & p ₂ & = (20 -20 ) 41 p ₁ p ₂= 400 41 aligned

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