Learn the two ellipse rules:

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

 

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 .  You can
always tell which is a² and which is b² because a² is ALWAYS
larger than b².


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

 

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 .  You can
always tell which is a² and which is b² because a² is ALWAYS
larger than b².
 

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



and get



or



The graph is 

 

Edwin