Points on circle

In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are integers. How many points is it?


n =  12


r1=2 cm (x0)2+(y0)2=r12 x2+y2=4  k:[2,0];[2,0];[0,2];[0,2]  r2=5 cm (x0)2+(y0)2=r22 x2+y2=25  l:[5,0];[5,0];[0,5];[0,5]; [3,4];[3,4];[3,4];[3,4] [4,3],[4,3],[4,3],[4,3]  n=3 4=12r_{1}=2 \ \text{cm} \ \\ (x-0)^2 + (y-0)^2=r_{1}^2 \ \\ x^2 + y^2=4 \ \\ \ \\ k: [2,0]; [-2,0]; [0,2]; [0,-2] \ \\ \ \\ r_{2}=5 \ \text{cm} \ \\ (x-0)^2 + (y-0)^2=r_{2}^2 \ \\ x^2 + y^2=25 \ \\ \ \\ l:[5,0]; [-5,0]; [0,5]; [0,-5]; \ \\ [3,4]; [3,-4]; [-3,4]; [-3,-4] \ \\ [4,3], [-4,3], [4,-3], [-4,-3] \ \\ \ \\ n=3 \cdot \ 4=12

The equation has the following integer solutions:
x^2 + y^2 = 25

Number of solutions found: 12
x1=-5, y1=0
x2=-4, y2=-3
x3=-4, y3=3
x4=-3, y4=-4
x5=-3, y5=4
x6=0, y6=-5
x7=0, y7=5
x8=3, y8=-4
x9=3, y9=4
x10=4, y10=-3
x11=4, y11=3
x12=5, y12=0

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Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Do you solve Diofant problems and looking for a calculator of Diofant integer equations?
Pythagorean theorem is the base for the right triangle calculator.

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