Question 191554
<pre><font size = 4 color = "indigo"><b>
Plot those 4 points:

{{{drawing(400,400,-2,11,-2,11,
graph(400,400,-2,11,-2,11),
line(4.9,6,5.1,6), line(5,5.9,5,6.1),
line(8.9,6,9.1,6), line(9,5.9,9,6.1),
line(6.9,3,7.1,3), line(7,2.9,7,3.1),
line(6.9,9,7.1,9), line(7,8.9,7,9.1)
  )}}}

Connect them to show the major and minor axes
of the ellipse:

{{{drawing(400,400,-2,11,-2,11,
graph(400,400,-2,11,-2,11), line(5,6,9,6), line(7,3,7,9) )}}}

Sketch in the ellipse:

{{{drawing(400,400,-2,11,-2,11,
graph(400,400,-2,11,-2,11), line(5,6,9,6), line(7,3,7,9), 
graph(400,400,-2,11,-2,11,6+(3/2)sqrt(4-(x-7)^2)),
graph(400,400,-2,11,-2,11,6-(3/2)sqrt(4-(x-7)^2))
)}}}

We can see that the ellipse has the standard form:

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

where 

1. (h,k) = the center 

2. a = the distance from the center to either end of the 
major axis.

3. b = the distance from the center to either end of the 
minor axis.

We can see from the graph that 

1. the center of the ellipse is (h,k) = (7,6)

2. a = 3

3. b = 2

So the equation 

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

becomes

{{{(x-7)^2/2^2 + (y-6)^2/3^2 = 1}}}

or

{{{(x-7)^2/4 + (y-6)^2/9 = 1}}}

Edwin</pre>