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

One and only one straight line can be drawn passing through two given points and we can draw only one triangle through non-collinear points. By integral coordinates (x,y) of a point we mean both x and y as integers . The number of points in the cartesian plane with integral coordinates satisfying the inequalities |x|le 4 , |y| le 4 and |x-y| le 4 is

Find the number of positive integral solutions satisfying the equation (x_(1)+x_(2)+x_(3))(y_(1)+y_(2))=77

The total number of integral points i.e. points having integral coordinates lying in the region represented by the inequations |x-y| lt 3 " and " |x+y| lt 3 is

The number of points with integral coordinates that lie in the interior of the region common to the circle x^(2)+y^(2)=16 and the parabola y^(2)=4x , is

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

The number of points with integral coordinates that are interior to the circle x^(2)+y^(2)=16 , is

Find the area of the region which is inside the parabola satisfying the condition |x-2 y|+|x+2y|le 8 and xy ge 2 .

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

Describe the locus of the point (x, y) satisfying the condition x^2 + y^2 =a^2 .