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AP EAMCET202022 Sep 2020Evening ShiftMathematicsApplication of DerivativesActual

Find the equation of normal to the curve y=x^3-3 x , which is parallel to the line 2 x+18 y=9 ?

Options

  1. Ax+9 y=20 only
  2. Bx+9 y=40 only
  3. Cx+9 y= 20
  4. Dx+9 y= 40

Correct answer

C. x+9 y= 20

Step-by-step solution

Given, line is 2 x+18 y=9 gathered slope (m)= -a b m= -2 18 =- 1 9 gathered Given equation of curve is y=x^3-3 x Differentiate w.r.to ' x ', we get d y d x =3 x^2-3 Slope of normal = -1 d y d x = -1 3 x^2-3 Since, normal is parallel to given line Slope of line = slope of normal aligned -1 9 & = -1 3 (x^2-1 ) x^2-1 & =3 x= 2 aligned Case (i) if x=2 from Eq. (i) aligned & y=(2)^3-3(2) y & =2 P & =(2,2) aligned Equation of normal is y-y₁=m (x-x₁ ) aligned y-2 & = -1 9 (x-2) x+9 y & =20 aligned Case (ii) If x=-2 aligne

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