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AP EAMCET202125 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

If two curves x=y^2, x y=a^3 cut each other orthogonally at a point, then a^2 is equal to

Options

  1. A1 3
  2. B1 2
  3. C2
  4. D3

Correct answer

B. 1 2

Step-by-step solution

Given, x=y^2 and x y=a^3 Solving, we get x=a^2 and y=a Now, y^2=x aligned & 2 y d y d x =1 d y d x = 1 2 y & ( d y d x )_ (a^2, a ) = 1 2 a & and x y=a^3 & x d y d x +y=0 & d y d x =- y x & ( d y d x )_ (a^2, a ) = -a a^2 = -1 a & aligned Curves intersect orthogonally. array rlrl & & ( d y d x )₁ ( d y d x )₂ & =-1 & ( 1 2 a ) ( -1 a ) & =-1 & a^2 & = 1 2 array

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