Points on circle

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

Correct answer:

n =  12

Step-by-step explanation:

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=12

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

Number of solutions found: 14
x1=-5; y1=0
x2=-5; y2=-0
x3=-4; y3=3
x4=-4; y4=-3
x5=-3; y5=4
x6=-3; y6=-4
x7=0; y7=5
x8=0; y8=-5
x9=3; y9=4
x10=3; y10=-4
x11=4; y11=3
x12=4; y12=-3
x13=5; y13=0
x14=5; y14=-0

Calculated by our Diofant problems and integer equations.

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