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AP EAMCET202021 Sep 2020Evening ShiftMathematicsApplication of DerivativesActual

If the tangent to the curve (x^ 2 / 3 +y^ 2 / 3 =a^ 2 / 3 ) meets the (X )-axis at (A ) and (Y )-axis at (B ), then (A B= )

Options

  1. A(2 a )
  2. B(3 a )
  3. Ca
  4. D(4 a )

Correct answer

C. a

Step-by-step solution

Given curve is (x^ 2 / 3 +y^ 2 / 3 =a^ 2 / 3 ) ...(i) Now, let a point on curve (P (a ^3 , a ^3 ) ) On differentiating the curve (i) w.r.t (x ), we get ( 2 3 x^ -1 / 3 + 2 3 y^ -1 / 3 d y d x =0 d y d x =- ( y x )^ 1 / 3 ) ( ) Slope of tangent at point (P ) is (m= . d y d x |_P=- ) ( ) Equation of the tangent of the curve at point (P ) is (y-a ^3 =- (x-a ^3 ) ...(ii) ) ( ) The tangent (ii) meets the axes at (A ) and (B ), so (A(a , 0) ) and (B(0, a ) ) ( A B= a^2 ^2 +a^2 ^2 =a ) Hence, option (c) is correct.

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