4. a) Radius of the Pony's path.
The equation of a circle whose center is not at the origin is given by the equation:
[tex](x-h)^2+(y-v)^2=r^2[/tex]
Where:
[tex]\bullet \ (h,v) \ is \ the \ center \\ \\ \bullet \ r \ is \ the \ radius[/tex]
According to the provided equation:
[tex](x-10)^2+(y-10)^2=10^2[/tex]
By comparing this equation with the previous one, we can assure that the radius is:
[tex]\boxed{r=10}[/tex]
