Question 756281
<pre>

We plot those points, and sketch the ellipse:

{{{drawing(400,240,-10,10,-6,6, graph(400,240,-10,10,-6,6),
circle(-8,0,.15),circle(-8,0,.14),circle(-8,0,.13),circle(-8,0,.12),
circle(-8,0,.11),circle(-8,0,.1),circle(-8,0,.09),circle(-8,0,.08),
circle(-8,0,.06),circle(-8,0,.05),

circle(0,0,.15),circle(0,0,.14),circle(0,0,.13),circle(0,0,.12),
circle(0,0,.11),circle(0,0,.1),circle(0,0,.09),circle(0,0,.08),
circle(0,0,.06),circle(0,0,.05),

circle(0,4,.15),circle(0,4,.14),circle(0,4,.13),circle(0,4,.12),
circle(0,4,.11),circle(0,4,.1),circle(0,4,.09),circle(0,4,.08),
circle(0,4,.06),circle(0,4,.05)  )}}}  {{{matrix(6,1,

SO,THE,ELLIPSE, LOOKS, LIKE, "THIS:")}}}  {{{drawing(400,240,-10,10,-6,6, graph(400,240,-10,10,-6,6),
circle(-8,0,.15),circle(-8,0,.14),circle(-8,0,.13),circle(-8,0,.12),
circle(-8,0,.11),circle(-8,0,.1),circle(-8,0,.09),circle(-8,0,.08),
circle(-8,0,.06),circle(-8,0,.05),

circle(0,0,.15),circle(0,0,.14),circle(0,0,.13),circle(0,0,.12),
circle(0,0,.11),circle(0,0,.1),circle(0,0,.09),circle(0,0,.08),
circle(0,0,.06),circle(0,0,.05),
arc(0,0,16,-8),
circle(0,4,.15),circle(0,4,.14),circle(0,4,.13),circle(0,4,.12),
circle(0,4,.11),circle(0,4,.1),circle(0,4,.09),circle(0,4,.08),
circle(0,4,.06),circle(0,4,.05)  )}}}  

Count the number of graph units there are between the center (0,0) 
and a vertex (-8,0). That's known as the "semi-major" axis, and its 
length is represented by the letter " a ".  So a = 8. [Incidentally
the ENTIRE major axis is 16 units long, it goes from one vertex (-8,0)
to the other vertex (8,0).]

Count the number of graph units there are between the center (0,0) 
and a covertex (0,4). That's known as the "semi-minor" axis, and its 
length is represented by the letter " b ".  So b = 4. [Incidentally
the ENTIRE minor axis is 8 units long, it goes from one covertex (0,4)
to the other covertex (0,-4).]

The equation of an ellipse that looks like this {{{drawing(20,10,-2,2,-1,1,arc(0,0,-3.9,1.9) )}}}

is    

          {{{(x-h)^2/a^2}}}{{{""+""}}}{{{(y-k)^2/b^2}}}{{{""=""}}}{{{1}}}

where (h,k) is the center (0,0)  so h=0, k=0, and a=8, b=4

          {{{(x-0)^2/8^2}}}{{{""+""}}}{{{(y-0)^2/4^2}}}{{{""=""}}}{{{1}}}

          {{{x^2/64}}}{{{""+""}}}{{{y^2/16}}}{{{""=""}}}{{{1}}}

Edwin</pre>