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AP EAMCET201921 Apr 2019Morning ShiftMathematicsApplication of DerivativesActual

The number of tangent to the curve y^2(x-a)=x^2(x+a)(a>0) that are parallel to the X -axis is

Options

  1. Ainfinitely many
  2. B0
  3. C1
  4. D2

Correct answer

B. 0

Step-by-step solution

Given, curve is y^2(x-a)=x^2(x+a) Apply log on both sides array ll & y^2(x-a = x^2(x+a) . & 2 y+ (x-a)=2 x+ (x+a) array Differentiating both sides w.r.t. x , we get 2 y d y d x + 1 x-a = 2 x + 1 x+a aligned & 2 y d y d x = 2 x + 1 x+a - 1 x-a & = 2(x+a)(x-a)+x(x-a)-x(x+a) x(x+a)(x-a) & = 2 (x^2-a^2 )+x^2-a x-x^2-a x x(x-a)(x+a) & 2 y d y d x = 2 x^2-2 a^2-2 a x x(x-a)(x+a) & d y d x = x^2-a^2-a x x(x-a)(x+a) x x+a x-a & At d y d x =0 & x^2-a^2-a x=0 & Here, p=a^2+4 a^2>0 & aligned So, it has two real roots.

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