Question 759157
The (main) vertices give you 'a', and the foci give you 'c'.  You use a and c to get an expression, and then a value for b.


Making a drawing and showing a triangle so one side is b, another side is c, the hypotenuse is a.  
{{{a^2=b^2+c^2}}}
{{{b^2=a^2-c^2}}}
and based on what you are given,
{{{b^2=8^2-6^2}}}
{{{b^2=28}}}


The center of the ellipse is the origin, so the equation is
{{{highlight(x^2/8^2+y^2/28=1)}}}