Question

which equation of a circle with center (5,0) that passes through the point (1,1)

Answer 1

its really the same as the distance from 5,0 to any (x,y), such that one of them is (1,1) :)

Answer 2

...the only things you really need to determine the equation of a circle is the center and the radius... one of which you already (explicitly) have.

Answer 3

\[(x-5)^2+(y-0)^2=r^2\]
plug in the point 1,1 to determine r

Answer 4

(1-5)^2+(1-0)^2=17