# 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?

Result

n =  12

#### Solution:

$r_{1}=2 \ \text{cm} \ \\ (x-0)^2 + (y-0)^2=r_{1}^2 \ \\ x^2 + y^2=4 \ \\ \ \\ k: [2,0]; [-2,0]; [0,2]; [0,-2] \ \\ \ \\ r_{2}=5 \ \text{cm} \ \\ (x-0)^2 + (y-0)^2=r_{2}^2 \ \\ x^2 + y^2=25 \ \\ \ \\ l:[5,0]; [-5,0]; [0,5]; [0,-5]; \ \\ [3,4]; [3,-4]; [-3,4]; [-3,-4] \ \\ [4,3], [-4,3], [4,-3], [-4,-3] \ \\ \ \\ n=3 \cdot \ 4=12$

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

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

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