Question 76855
<pre><font size = 4><b>
Learn the two ellipse rules:

1. An ellipse with major axis parallel to the x-axis has equation

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

Where (h,k) is the center, "a" is one-half the major axis and
and "b" is one-half the minor axis.  The foci are the points
(h+c,k) and (h-c,k) where {{{c = sqrt(a^2+b^2)}}}.  You can
always tell which is aČ and which is bČ because aČ is ALWAYS
larger than bČ.


2. An ellipse with major axis parallel to the y-axis has equation

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

Where (h,k) is the center, "a" is one-half the major axis and
and "b" is one-half the minor axis.  The foci are the points
(h,k+c) and (h,k-c) where {{{c = sqrt(a^2+b^2)}}}.  You can
always tell which is aČ and which is bČ because aČ is ALWAYS
larger than bČ.
 

Your problem is on the first type

an ellipse with major axis 6 units long and parallel to the 
x-axis; minor axis 4 units long; and center at (8,6)

a = 1/2 the major axis = (1/2)(6) = 3
b = 1/2 the minor axis = (1/2)(4) = 2
(h,k) = (8,6)

Substitute in

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

and get

{{{(x-8)^2/3^2+(y-6)^2/2^2=1}}}

or

{{{(x-8)^2/9+(y-6)^2/4=1}}}

The graph is 

{{{graph( 300, 212, -2, 15, -2, 10, 0, 0, sqrt(4-4(x-8)^2/9)+6,0, -sqrt(4-4(x-8)^2/9)+6) }}} 

Edwin</pre>