If `2x^2-3x y-2y^2=7,` then prove that there will be only two integral pairs `(x ,y)` satisfying the above relation.

Find the number of integral ordered pairs (x,y) satisfying the equation log(3x+2y)=logx+logy.

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

If point (x,y) satisfy the relation x^2+4y^2-4x+3=0 then

x+7y=10 3x-2y=7

Number of ordered pair (x, y) satisfying x^(2)+1=y and y^(2)+1=x is

Find the greatest and the least real value of x$ y satisfy the relation x^(2)+y^(2)=6x-8y

For x in[-2 pi,3 pi] and y in R, the number of ordered pairs (x,y) satisfying the equation sqrt(3)sin x-cos x-3y^(2)+6y-5=0, is equal to

Find the number of point (x,y) having integral coordinates satisfying the condition x^(2)+y^(2)<25

The number of points (x.y) satisfying 3y+4x=20 and x^(2)+y^(2)<16