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AP EAMCET202124 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

Find the area of the triangle formed by the X -axis and the tangent and the normal to the curve x^2 a^2 + y^2 b^2 =1 at the point ( a 2 , b 2 )

Options

  1. Aa b 4 a^2+b^2
  2. B4 a b
  3. Cb 4 a (a^2+b^2 )
  4. Da b 2 a^2+b^2

Correct answer

C. b 4 a (a^2+b^2 )

Step-by-step solution

Ellipse, x^2 a^2 + y^2 b^2 =1...(i) To find Equation of tangent and normal at point ( a 2 , b 2 ) We have to find d y d x . Slope of tangent = . d y d x |_ ( a 2 , b 2 ) =m_T Now, differentiating Eq. (i) w.r.t. x aligned 2 x a^2 + 2 y b^2 d y d x & =0 d y d x & =- 2 x a^2 2 y b^2 =- b^2 a^2 ( x y ) aligned aligned & m_T=- b^2 a^2 ( a 2 b 2 )=- b a & and m_N=- 1 m_T = a b aligned Equation of tangent (y- b 2 )=- b a (x- a 2 )...(ii) Equation of normal (y- b 2 )= a b (x- a 2 )...(iii) To find Area of triangle made by

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