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?

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: 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

Calculated by our Diofant problems and integer equations.



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