Question 920729
{{{x^2+y^2=R^2}}}<--->{{{x^2/R^2+y^2/R^2=1}}} is the equation of a circle of radius {{{R}}} centered at (0,0).
Since {{{x^2<=x^2+y^2=R^2}}} , {{{x^2<=R^2}}} and {{{-R<=x<=R}}} .
Similarly, since {{{y^2<=x^2+y^2=R^2}}} , {{{y^2<=R^2}}} and {{{-R<=y<=R}}} .
An ellipse is just a circle stretched more in one direction than the other.
In your case, you will have vertices at (0,-10) and (0,10),
meaning that {{{-10<=y<=10}}} ,
and co-vertices at (-6,0) and (6,0),
meaning that {{{-6<=x<=6}}} .
A circle with radius {{{6}}} would have the equation {{{x^2/6^2+y^2/6^2=1}}} ,
and all its points would have to comply with
{{{-6<=x<=6}}} and {{{-6<=y<=6}}} .
We want {{{-6<=x<=6}}} for the x coordinates,
but {{{-10<=y<=10}}} for the y coordinates,
so the equation for the ellipse is
{{{x^2/6^2+y^2/10^2=1}}} .