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AP EAMCET202317 May 2023Morning ShiftMathematicsApplication of DerivativesActual

If (a^2-1 ) x+a y+(3-a)=0 is a normal to the curve x y=1 , then the interval in which ' a ' lies is

Options

  1. A[-1,1] [2, )
  2. B(- ,-1] (0,1]
  3. C[-1,1) (1, )
  4. D(1, )

Correct answer

B. (- ,-1] (0,1]

Step-by-step solution

x y=1 d y d x =- 1 x^2 Slope of normal of x y=1 is m=x^2 0...(i) Equation of normal is aligned & (a^2-1 ) x+a y+(3-a)=0 & m= d y d x =- 1-a^2 a From (i) & m 0 & 1-a^2 a 0 a (- ,-1] (0,1] aligned

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