The number of positive integral pairs (x, y) satisfying the equation ` x^(2) - y^(2) = 3370 ` is :

The number of integral pairs (x, y) satisfying the equation 2x^(2)-3xy-2y^(2)=7 is :

The number of ordered pairs of integers (x,y) satisfying the equation x ^2+6x+y^2 =4 is

The number of positive integral solutions (x,y) of the equation 2xy-4x^(2)+12x-5y=11, is

The number of positive integral solutions (x,y) of the equation 2xy-4x^(2)+12x-5y=11, is

The number of positive integral solutions of the equation x+2y+z=25 is

The number of ordered pair (x, y) satisfying the equation sin^(2) (x+y)+cos^(2) (x-y)=1 which lie on the circle x^(2)+y^(2)=pi^(2) is _________.

The number of ordered pair (x, y) satisfying the equation sin^(2) (x+y)+cos^(2) (x-y)=1 which lie on the circle x^(2)+y^(2)=pi^(2) is _________.

The number of ordered pair (x, y) satisfying the equation sin^(2) (x+y)+cos^(2) (x-y)=1 which lie on the circle x^(2)+y^(2)=pi^(2) is _________.

If x, y in [0, 2 pi] , then the total number of ordered pairs (x, y) satisfying the equation sinx cos y = 1 is