Question 752402
You want to fill in {{{x^2/a^2+y^2/b^2=1}}} with the particular values.  Center is at the origin so no need to worry about x and y translation.  The focal distance according to your given foci is c=8.


If eccentricity is 4/5, then you have {{{4/5=c/a}}}.  You can find a.
{{{a/c=5/4}}}
{{{a=5c/4=5*8/4=highlight(10)}}}


Next, find b.  {{{a^2=b^2+c^2}}}
{{{b^2=a^2-c^2}}}
You do not quite need b for filling in that part of the equation but you still have the value in the form of its square.  {{{b^2=10^2-8^2=100-64=highlight(36)}}}


Equation is {{{highlight(x^2/64+y^2/36=1)}}}