Answer:
[tex]\large\boxed{(x-8)^2+(y-6)^2=6^2\to(x-8)^2+(y-6)^2=36}[/tex]
Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the center (8, 6) → h = 8, k = 6,
and endpoints of a radius (8, 6) & (8, 0).
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute:
[tex]r=\sqrt{(0-6)^2+(8-8)^2}=\sqrt{(-6)^2+0^2}=\sqrt{36}=6[/tex]
Finally:
[tex](x-8)^2+(y-6)^2=6^2[/tex]
