Answer
See below
Work Step by Step
Given $x^2+y^2-8y+16x+16=0$
We can see that $a=1\\b=0\\c=1$
We will find the discriminant of the given equation $=b^2-4ac\\=0^2-4(1)(1)\\=0$
Since $-4\lt 0$ and $a=c$, the conic is a circle.
To graph the circle, first complete the square:
$x^2+y^2-8y+16x+16=0\\x^2+y^2-8y+16x=-16\\(x^2+16x+64)-64+(y^2-8y+16)-16=-16\\(x+8)^2+(y-4)^2=64$
From the equation, you can see that the center is at $(-8,4)$ and the radius is $r=8$
