Number of pairs `(x,y)` real number that satisfy `2x^2+y^2+2x y-2y+2=0,` is

The number of ordered pairs (x, y) of real number satisfying 4x^2 - 4x + 2 = sin^2 y and x^2 + y^2 <= 3 equal to

The number of ordered pairs (x, y) of real number satisfying 4x^2 - 4x + 2 = sin^2 y and x^2 + y^2 <= 3 equal to

The number of ordered pairs (x,y) of real numbers that satisfy the simultaneous equations x+y^(2)=x^(2)+y=12 is

The number of ordered pairs (x,y) of real number satisfying 4x^(2)-4x+2=sin^(2)y and x^(2)+y^(2)<=3 equal to

The number of distinct pairs (x,y) of the real number satisfying x=x^(3)+y^(4) and y=2xy is

The number of pairs (x, y) of real numbers with 0 lt x lt (pi)/( 2) " that " ((sin x)^(2y))/((cos x)^((y^(2))/(2)))+((cos x)^(2y))/((sin x) ^((y^(2))/(2)))= sin 2 x is equal to

The number of distinct pairs (x,y) of the real number satisfying x=x^(3)+y^(4)and y=2xy is :

The number of distinct pairs (x,y) of the real number satisfying x=x^(3)+y^(4)and y=2xy is :

The number of ordered pair(s) (x, y) of real numbers satisfying the equation 1+x^(2)+2x sin(cos^(-1)y)=0 , is :