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Manipal MET2017MathematicsHyperbola

Consider the hyperbola x^2 a^2 - y^2 b^2 =1 the area of the triangle formed by the asymptotes and the tangent drawn to it at (a, 0) is

Options

  1. A1 2 a b
  2. Ba b
  3. C2 a b
  4. D4ab

Correct answer

B. a b

Step-by-step solution

Equation of tangent at (a, 0) is x=a and the point of intersection of x=a and the asymptotes will be obtained by solving x=a and the equation of asymptotes b x a y=0 a b a y=0 y= b Now, point of intersections are (a, b) and (a,-b) . Area of triangle = 1 2 (a b 2)=a b sq unit

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