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AP EAMCET201922 Apr 2019Morning ShiftMathematicsArea Under CurvesActual

If the area of the region bounded by the curves (y=x^2 ) and (x=y^2 ) is (k ), then the area of the region bounded by the curves ( x+ 3 y 2 = ( 3 x-y 2 )^2 ) and ( 3 x-y 2 = ( x+ 3 y 2 )^2 ), is

Options

  1. A( 3 2 k )
  2. B( 1 2 k )
  3. C(k )
  4. D( ( 3 +1 2 ) k )

Correct answer

C. (k )

Step-by-step solution

Let ( x+ 3 y 2 = x+ 3 y 1+( 3 )^2 =y ) and ( 3 x-y 2 = 3 x-y ( 3 )^2+1 =x ) so, the given curve ( x+ 3 y 2 = ( 3 x-y 2 )^2 ), becomes (y=x^2 )...(i) Similarly, the given curve ( 3 x-y 2 = ( x+ 3 y 2 )^2 ), becomes (x^2=y )...(ii) So the area of the region bounded by curves (i) and (ii) is equals to the area of the region bounded by the curve (y=x^2 ) and (x=y^2 ) is equal to ‘ (K ) ' (given).

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