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AP EAMCET202318 May 2023Morning ShiftMathematicsApplication of DerivativesActual

The slope of the tangent at any point (x, y) on the curve, is equal to the product of the coordinates of that point. If the equation of the normal to the curve at the point ( 2 , e) is a x+b y=1 , then b a =

Options

  1. A1 2 e
  2. Be 2
  3. C2 e
  4. D2 e

Correct answer

C. 2 e

Step-by-step solution

Slope of tangent at point ( 2 , e ) is m = e 2 Then, slope of normal, m^ =- 1 m =- 1 e 2 Equation of normal at point ( 2 e ) : (y-e)=m^ (x- 2 ) aligned & y-e=- 1 e 2 (x- 2 ) & e 2 y-e^2 2 =-x+ 2 & x+e 2 y= 2 +e^2 2 aligned x 2 (e^2+1 ) + e 2 2 (e^2+1 ) y=1 ...(i) Given equation of normal is, a x+b y=1 ...(ii) Then a= 1 2 (e^2+1 ) and b= e 2 2 (e^2+1 ) b a = e 2 1 = 2 e

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