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The area (in sq. units) of the triangle formed by the lines y = 2 x , y = - 2 x and the tangent at the point 5 , 4 on 4 x 2 - y 2 = 4 is equal to

Options

  1. A4
  2. B2
  3. C1
  4. D3

Correct answer

B. 2

Step-by-step solution

Equation of the tangent at point 5 , 4 on 4 x 2 - y 2 = 4 is 4 x 5 - 4 y = 4 ⇒ 5 x - y = 1 . Now, point of intersection of y = 5 x - 1   &   y = 2 x is 1 5 - 2 , 2 5 - 2 . Point of intersection of y = 5 x - 1 and y = - 2 x is 1 5 + 2 , - 2 5 + 2 . Point of intersection of y = 2 x & y = - 2 x is 0,0 Now, area of the triangle formed by the points 0,0 , 1 5 - 2 , 2 5 - 2 , 1 5 + 2 , - 2 5 + 2 = 1 2 0 0 1 1 5 - 2 2 5 - 2 1 1 5 + 2 - 2 5 + 2 1 = 1 2 × 1 × - 2 - 2 = 2 sq.units

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