Graph

We want to put $x^2+y^2=2x-6y+16+14x-4y+20$ in the form of a circle's equation. 

Moving all terms to one side, we get $x^2-16x+y^2+10y=36$

Completing the square for both x and y, we get $(x-8)^2+(y+5)^2=125$

$\left(x-8\right)^2+\left(y+5\right)^2=\left(5\sqrt{5}\right)^2$

From this, we get that $5\sqrt5$ is the radius. 

The area is $\pi r^2 = \pi (125) = 125\pi$

125pi is our answer

Thanks! :)