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AP EAMCET202317 May 2023Evening ShiftMathematicsStraight LinesActual

If t R - -1 , then the locus of the point ( 3 a t 1+t^3 , 3 at ^2 1+t^3 ) is

Options

  1. Ax ^3+ y ^3=3 a x ^2 y ^2
  2. Bx^3-3 a x^2 y-3 a x y^2+y^3=0
  3. Cx^3+y^3=3 a x y
  4. Dx^3-y^3=3 a x y

Correct answer

C. x^3+y^3=3 a x y

Step-by-step solution

Here, x= 3 a t 1+t^3 , y= 3 a t^2 1+t^3 aligned & x^3+y^3= ( 3 a t 1+t^3 )^3+ ( 3 a t^2 1+t^3 )^3 & = ( 3 a t 1+t^3 )^3 (1+ t ^3 ) & = (3 a t)^3 (1+ t ^3 )^2 = 3 a 3 a t 3 a t^2 (1+ t ^3 )^2 =3 a x y aligned

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