Question 1003727
You have the definition, so just use the Distance Formula and simplify into the standard form equation for the ellipse.  This means, DERIVE the equation starting with the use of Distance Formula.


The points on the ellipse are some set of unknown points, (x,y).


Initial Set-up, {{{sqrt((x-(-3))^2+(y-0)^2)+sqrt((x-3)^2+(y-0)^2)=8}}}


Beginning steps,
{{{sqrt((x+3)^2+(y)^2)+sqrt((x-3)^2+(y)^2)=8}}}


{{{sqrt((x+3)^2+y^2)+sqrt((x-3)^2+y^2)=8}}}


{{{sqrt((x+3)^2+y^2)=8-sqrt((x-3)^2+y^2)}}}


First Squaring of both sides,
{{{(x+3)^2+y^2=8^2-16sqrt((x-3)^2+y^2)+(x-3)^2+y^2}}}
...
...
...and thirteen more steps done on paper which will be difficult to type-in all the text of them here; lead to {{{highlight(x^2/16+y^2/7=1)}}}.