Answer:
center: (8, 0)
radius: 10
Step-by-step explanation:
The equation of a circle in a standard form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the equation:
[tex]x^2-16x+y^2=36\\\\x^2-2(x)(8)+y^2=36\qquad\text{add}\ 8^2\ \text{to both sides}\\\\\underbrace{x^2-2(x)(8)+8^2}_{(*)}+y^2=36+8^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\qquad(*)\\\\(x-8)^2+(y-0)^2=36+64\\\\(x-8)^2+(y-0)^2=100\\\\(x-8)^2+(y-0)^2=10^2\\\\\text{Therefore}\\\\center:(8,\ 0)\\radius:10[/tex]
