write an equation for the 
ellipse that satisfies each set of conditions.
endpoints of major axis at (-9,0) and (9,0), 
endpoints of minor axis at (0,3) and (0,-3).

Its center is at the origin because (0,0) is halfway 
between both the endpoints of the major axis as well 
as halfway between both endpoints of the minor axis, 
therefore the equation is either of the form

 x²     y²
---- + ---- = 1
 a²     b²

if it is fatter than it is tall, that is, like
an egg lying on a table,

      or

 x²     y²
---- + ---- = 1
 b²     a²

if it is taller than it is fat, that is, like
the numeral zero, 0.

Obviously this one is like an egg lying on a table.

a = half the major axis
b = half the minor axis

the distance between (-9,0) and (9,0) is 18 and
the distance between (-3,0) and (3,0) is 6

so a = 9 and b = 3

So the equation is

 x²     y²
---- + ---- = 1
 a²     b²

or

 x²     y²
---- + ---- = 1
 9²     3²
 
or

 x²     y²
---- + ---- = 1
 81     9

Its graph is:

 

Edwin