Answer:
A. [tex](x-4)^2+(y-3)^2=25[/tex]
Step-by-step explanation:
Radius:
The length of diameter[tex](d)[/tex] is the distance between A and B.
[tex]d=\sqrt{(8-0)^2+(6-0)^2}=\sqrt{64+36}=\sqrt{100}=10\\\\radius(r)=\frac{d}{2}=\frac{10}{2}=5[/tex]
Centre:
Since A and B are end points of the diameter, centre is the mid point of these two. Let [tex](x,y)[/tex] be the centre of the circle.
[tex]x=\frac{8+0}{2}=4\\\\y=\frac{6+0}{2}=3\\\\[/tex]
Centre is [tex](4,3)[/tex]
Equation of circle:
If [tex](a,b)[/tex] is the centre of the circle and [tex]r[/tex] be the radius. Equation of circle is given by:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
[tex]Here\ (a,b)=(4,3)\ and\ r=5\\Equation:\ (x-4)^2+(y-3)^2=5^2\\(x-4)^2+(y-3)^2=25[/tex]
