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JEE Main2017MathematicsApplication of DerivativesActual

The tangent at the point ( 2 , - 2 ) to the curve, x 2 y 2 - 2 x = 4 1 - y does not pass through the point:

Options

  1. A- 2 , - 7
  2. B8 , 5
  3. C- 4 , - 9
  4. D4 , 1 3

Correct answer

A. - 2 , - 7

Step-by-step solution

Given curve x 2 y 2 - 2 x = 4 - 4 y Differentiate both sides w.r.t x , ⇒ 2 x y 2 + 2 y . x 2 . d y d x - 2 = - 4 . d y d x ⇒ d y d x 2 y . x 2 + 4 = 2 - 2 x . y 2 ⇒ d y d x 2 , - 2 = 2 - 2 × 2 × 4 2 - 2 × 4 + 4 = 14 12 = 7 6 Equation of tangent, y + 2 = 7 6 x - 2 ⇒ 7 x - 6 y = 26 , which doesn't pass through - 2 - 7 .

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