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NTA Abhyas JEE Main2020MathematicsHyperbolaPractice

The area of triangle formed by the lines x - y = 0 , x + y = 0 and any tangent to the hyperbola x 2 - y 2 = 16 is equal to

Options

  1. A2 sq. units
  2. B4 sq. units
  3. C8 sq. units
  4. D16 sq. units

Correct answer

D. 16 sq. units

Step-by-step solution

Equation of the tangent to the hyperbola x 2 - y 2 = 16 in parametric form is 4 x sec ⁡ ϕ - 4 y tan ⁡ ϕ = 16 ⇒ x sec ⁡ ϕ - y tan ⁡ ϕ = 4 Solving with y = x and y = - x , we get, A 4 sec ⁡ ϕ + tan ⁡ ϕ , 4 sec ⁡ ϕ + tan ⁡ ϕ , B 4 sec ⁡ ϕ - tan ⁡ ϕ , 4 tan ⁡ ϕ - sec ⁡ ϕ ∴ Area bounded by ∆ A O B = 1 2 16 tan 2 ⁡ ϕ - sec 2 ⁡ ϕ - 16 sec 2 ⁡ &#98

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