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JEE Main2017MathematicsApplication of DerivativesActual

The normal to the curve y x - 2 x - 3 = x + 6 at the point where the curve intersects the y -axis passes through the point:

Options

  1. A- 1 2 , - 1 2
  2. B1 2 , 1 2
  3. C1 2 , - 1 3
  4. D1 2 , 1 3

Correct answer

B. 1 2 , 1 2

Step-by-step solution

To find the point where curve intersects the y-axis Put, x = 0 , we get 6 y = 6 ⇒ y = 1 Hence, the point is (0, 1). On differentiating ⇒ d y d x   x - 2   x - 3 + y 2 x - 5 = 1 Put, x = 0 ,   y = 1 , we get ⇒   d y d x + 6 + 1 - 5 = 1 ⇒ d y d x = 1 ⇒ Slope of normal = - 1 Equation of normal at 0 ,   1 ⇒ y - 1 = - 1 x - 0 ⇒ x + y - 1 = 0 Point 1 2 , 1 2 satisfy the normal.

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