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AP EAMCET202423 May 2024Morning ShiftMathematicsApplication of DerivativesActual

If the length of the sub-tangent at any point P on a curve is proportional to the abscissa of the point P. then the equation of that curve is ( C is an arbitrary constant)

Options

  1. Ay^k+x^k=C
  2. Bx^ 1 / k C=y^k
  3. C(x+y)^k=C
  4. Dy=x^ 1 / k C

Correct answer

D. y=x^ 1 / k C

Step-by-step solution

Length of sub-tangent = y d y d x According to question, y d y d x =k x d x k x = d y y y= 1 k x+ C y=x^ 1 / k C

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