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BITSAT2019MathematicsApplication of DerivativesActual

The distance between the origin and the normal to curve y = e 2 x + x 2 at x = 0 is

Options

  1. A2 3
  2. B2 5
  3. C1 3
  4. D1 5

Correct answer

B. 2 5

Step-by-step solution

We have, y = e 2 x + x 2 at x = 0 , y = 1 d y d x = 2 e 2 x + 2 x d y d x x = 0 = 2 ∴ Equation of normal at ( 0 , 1 ) is y - 1 = - 1 2 ( x ) ⇒   x + 2 y - 2 = 0 ∴ Distance from ( 0 , 0 ) from normal = 2 5

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