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AP EAMCET202316 May 2023Morning ShiftMathematicsApplication of DerivativesActual

If the tangent drawn at A(2,1) to the curve x =1+ 1 y ^2 meets the curve again at B , then

Options

  1. Athe tangent drawn at B coincides with the tangent drawn at A
  2. Bthe angle between the tangents drawn at A and B is neither 0 nor 2
  3. Cthe tangent drawn at A and the tangent drawn at B are perpendicular to each other
  4. Dthe tangent drawn at A is parallel to the tangent drawn at B

Correct answer

B. the angle between the tangents drawn at A and B is neither 0 nor 2

Step-by-step solution

The given curve is : x=1+ 1 y^2 ...(i) 1=-2 1 y^3 y^ y^ = -y^2 2 (y^ )_ (2,1) =- 1 2 . The equation of tangent at point (2,1)(y-1)=- 1 2 (x-2) y-2=- 1 2 x x=4-2 y ...(ii) We can get the point B by solving (i) and (ii) 4-2 y=1+ 1 y^2 2 y^3-3 y^2+1=0 aligned & (y-1)^2(2 y+1)=0 & y=- 1 2 , 1,1 aligned For point B, y=- 1 2 At y=- 1 2 , x=1+4=5 Co-ordinate of B (5,- 1 2 ) Let us find the equation of tangent at B (5,- 1 2 ) (y+ 1 2 )=- 1 8 (x-5) y=- 1 8 x+ 1 8 ...(iii) Eqns. (ii) and (iii) are not same. So, option (1) is

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