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AP EAMCET202119 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

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

Options

  1. A2
  2. B2 3
  3. C2 5
  4. D1 2

Correct answer

C. 2 5

Step-by-step solution

Given curve is y = e 2 x   +   x 2 When x   =   0   ⇒   y   =   1 d y d x   =   2 e 2 x   +   2 x At 0 ,   1 d y d x   =   2 Slope of normal   =   - d x d y   =   - 1 2 Equation of normal is y   -   1   =   - 1 2   x - 0 2 y   -   2   =   - x x   +   2 y   - 2   =   0 Distance from origin to line is c a 2 + b 2 =   2 5

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