The equation of the ellipse that has a center at (8,4)\displaystyle {\left({8},{4}\right)}, a focus at (12,4)\displaystyle {\left({12},{4}\right)}, and a vertex at (3,4)\displaystyle {\left({3},{4}\right)}, is
(xC)2A2+(yD)2B2=1\displaystyle {\frac{{{\left({x}-{C}\right)}^{{2}}}}{{{A}^{{2}}}}}+{\frac{{{\left({y}-{D}\right)}^{{2}}}}{{{B}^{{2}}}}}={1}
where
A=\displaystyle {A}=  
B=\displaystyle {B}=  
C=\displaystyle {C}=  
D=\displaystyle {D}=