so hmm check the picture below
the diameter has those endpoints, recall the radius is half the diameter
the diameter length is [tex]\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 0}}\quad ,&{{ 4}})\quad
% (c,d)
&({{ 6}}\quad ,&{{ -4}})
\end{array}\qquad
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}[/tex]
the radius is half that
and the center will be half-way on that segment, namely, the MidPoint
so the center will be at [tex]\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 0}}\quad ,&{{ 4}})\quad
% (c,d)
&({{ 6}}\quad ,&{{ -4}})
\end{array}\qquad
% coordinates of midpoint
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)\\\\
-----------------------------\\\\
h=\cfrac{{{ x_2}} + {{ x_1}}}{2}\qquad \qquad k=\cfrac{{{ y_2}} + {{ y_1}}}{2}[/tex]
so plug those three[tex]\bf (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad center\ ({{ h}},{{ k}})\qquad
radius={{ r}}[/tex] at
