Answer
The equation of the circle is $(x-5)^2+(y-5)^2=25$ and the line's equation is $y=-{4\over3}x+{35\over3}$
Work Step by Step
The standard equation of a circle is $(x-h)^2+(y-k)^2=r^2$ where $(h, k)$ is the center of the circle and $r$ is the radius. Since the center is at the point $(5,5)$, $h$ and $k$ are both $5$. We can also see that the radius is $5$
Now we can fill in the standard equation with the values found:
$(x-5)^2+(y-5)^2=5^2$ --> $(x-5)^2+(y-5)^2=25$
To find the line's equation, we'll first find its slope. To do so, we'll use the points $(5,5)$ and $(8,1)$ in the equation $m={y_{1}-y_{2}\over x_{1}-x_{2}}$
$m={5-1 \over 5-8}=-{4\over3}$
Now, we'll use the point $(5,5)$ and the slope $m$ in the standard form $y=mx+b$ to find $b$ and then the line's equation.
$5=-{4\over 3} \cdot (5)+b$ --> ${15\over 3}+{20\over 3}=b={35\over3}$
$y=-{4\over3}x+{35\over3}$
