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AP EAMCET202123 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

If the tangent to the curve 2 y^3=a x^2+x^3 at the point (a, a) cuts off intercepts and on the coordinate axes, where ^2+ ^2=61 , then the value of |a| is

Options

  1. A14
  2. B30
  3. C20
  4. D25

Correct answer

B. 30

Step-by-step solution

Given curve, 2 y^3=a x^2+x^3 and ^2+ ^2=61 Let A(a, a) be the point. Differentiate Eq. (i) w.r.t x we get aligned 6 y^2 d y d x & =2 a x+3 x^2 d y d x & = a x 3 y^2 + x^2 2 y^2 ( d y d x )_ (a, a) & = a^2 3 a^2 + a^2 2 a^2 = 1 3 + 1 2 = 5 6 aligned Now, slope of line at (a, a)=5 / 6 Equation of line is array rlrl y-y₁ & =m (x-x₁ ) & y-a & = 5 6 (x-a) or 6 y-5 x=a & y a / 6 - x a / 5 & =1 or x -a / 5 + y a / 6 =1 array Compare with intercept form of line x + y =1 Gives =- a 5 , = a 6 Given, ^2+ ^2=61 aligned & = a^2

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