I need to find the coordinates of two vertices with focal points of $(2, 6)$ and $(8, -2)$ and the distance between the vertices is $18$.
I was able to calculate the center of the ellipse which is the midpoint of the foci: $(5, 2)$. I also know that that the $a$ value (the distance from one of the vertices on the major axis to the center) is going to be $9$ since the $c$ value is $5$. I can therefore say that whatever the coordinates of the vertices are must be $4$ units away from the two focal points. However, I am not able to get any further than that in finding the coordinates of the vertices. Any help will be greatly appreciated.