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AP EAMCET202318 May 2023Morning ShiftMathematicsApplication of DerivativesActual

The area (in sq units) of the triangle formed by the normal drawn at the point (1,0) on the curve x = e ^ y with the coordinate axes is

Options

  1. A1
  2. B1 4
  3. C1 2
  4. D3 8

Correct answer

C. 1 2

Step-by-step solution

x=e^ y x= y 1 x = y d y d x d y d x = 1 x y Slope of normal at (1,0)=- 1 ( d y d x )_ (1,0) =- .x y |_ (1,0) m=-1 0=-1 Equation of normal to curve at (1,0) : (y-0)=m(x-1) y=-(x-1) x+y=1 OBA is the required region, whose area we have to calculate Area = 1 2 OB OA = 1 2 1 1= 1 2 ( . unit .^2 )

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