Answer:
The equation of the circle is [tex](x-4)^{2}+(y)^{2} =100[/tex]
Step-by-step explanation:
we know that
The general equation of the circle into center-radius form is equal to
[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]
where
(h,k) is the center of the circle
In this problem
[tex](h,k)=(4,0)[/tex]
substitute
[tex](x-4)^{2}+(y-0)^{2} =r^{2}[/tex]
[tex](x-4)^{2}+(y)^{2} =r^{2}[/tex]
Find the radius
we know that
The distance between the points (-2,8) and (4,0) is equal to the radius
Applying the distance 's formula
[tex]d=\sqrt{(0-8)^{2}+(4+2)^{2}}[/tex]
[tex]d=\sqrt{100[/tex]
[tex]d=10\ units[/tex]
so
the radius is equal to [tex]r=10\ units[/tex]
substitute
[tex](x-4)^{2}+(y)^{2} =10^{2}[/tex]
[tex](x-4)^{2}+(y)^{2} =100[/tex]
