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.

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 ordered pairs of natural numbers (x, y) satisfying the equation: (xy-1)^(2) = (x+1)^(2) + (y+1)^(2)

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