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NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

The tangent at any point on the curve x y = 4 makes intercepts on the coordinate axes as a and b . Then the value of a b is

Options

  1. A8
  2. B16
  3. C32
  4. D64

Correct answer

B. 16

Step-by-step solution

Let P h , k be a point on x y = 4 ⇒ h k = 4 … 1 Differentiating x y = 4 w.r.t. x , we get, x d y d x + y = 0 ⇒ d y d x = - y x The slope of the tangent at P h , k = - k h So, the equation of the tangent is k x + h y = 2 h k ⇒ k x + h y = 8 (from ( 1 ) ) x - intercept = - 8 k , y - intercept = - 8 h Hence, a b = 64 h k = 64 4 = 16

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