Question 1103542
<pre>
We plot the center and focus:

{{{drawing(400,300,-4,4,-3,3,graph(400,300,-4,4,-3,3),circle(2,0,.08),circle(2,0,0.04), circle(0,0,.08),circle(0,0,0.04))}}}

So we know that c = 2 since c is the distance 
from the center to the focus.  

We also know that the ellipse is like this {{{drawing(20,10,-2,2,-1,1,arc(0,0,-3.9,1.9) )}}}
so its equation is {{{x^2/a^2+y^2/b^2=1}}}

We also know that the other focus is 2 units on the 
left of the center, at (-2,0) so we plot that too:

{{{drawing(400,300,-4,4,-3,3,graph(400,300,-4,4,-3,3),circle(2,0,.08),circle(2,0,0.04), circle(0,0,.08),circle(0,0,0.04),circle(-2,0,.08),circle(-2,0,0.04))}}}

Since we know that 7/3 is one-half length of the minor axis,
that means that that b = 7/3, the semi-minor axis.

So we know that the top point (sometimes called the top covertex)
is (0,7/3), so we plot that too, as well as the other covertex at
(0,-7/3):

{{{drawing(400,300,-4,4,-3,3,graph(400,300,-4,4,-3,3),circle(2,0,.08),circle(2,0,0.04), circle(0,0,.08),circle(0,0,0.04),circle(-2,0,.08),circle(-2,0,0.04),
circle(0,7/3,.08),circle(0,7/3,0.04),circle(0,-7/3,.08),circle(0,-7/3,0.04)

)}}}

The ellipse equation for a,b, and c is {{{a^2-b^2=c^2}}}, so

{{{a^2-b^2=c^2}}}
{{{a^2-(7/3)^2=(2)^2}}}
{{{a^2=(2)^2+(7/3)^2}}}
{{{a^2=4+49/9}}}
{{{a^2=36/9+49/9}}}
{{{a^2=85/9}}}
{{{a=sqrt(85)/3}}}

That's about 3.073, so we plot the vertices, too,
at {{{"" +- sqrt(85)/3}}}

{{{drawing(400,300,-4,4,-3,3,graph(400,300,-4,4,-3,3),circle(2,0,.08),circle(2,0,0.04), circle(0,0,.08),circle(0,0,0.04),circle(-2,0,.08),circle(-2,0,0.04),
circle(0,7/3,.08),circle(0,7/3,0.04),circle(0,-7/3,.08),circle(0,-7/3,0.04),
circle(sqrt(85)/3,0,.08),circle(sqrt(85)/3,0,0.04),circle(-sqrt(85)/3,0,.08),circle(-sqrt(85)/3,0,0.04)

)}}}

So the equation 

{{{x^2/a^2+y^2/b^2=1}}}

becomes:

{{{x^2/(85/9)+y^2/2^2=1}}}

{{{x^2/(85/9)+y^2/4=1}}}

You can simplify it to 

{{{36x^2 + 85y^2 = 340}}}

if you like.

{{{drawing(400,300,-4,4,-3,3,graph(400,300,-4,4,-3,3),circle(2,0,.08),circle(2,0,0.04), circle(0,0,.08),circle(0,0,0.04),circle(-2,0,.08),circle(-2,0,0.04),
circle(0,7/3,.08),circle(0,7/3,0.04),circle(0,-7/3,.08),circle(0,-7/3,0.04),
circle(sqrt(85)/3,0,.08),circle(sqrt(85)/3,0,0.04),circle(-sqrt(85)/3,0,.08),circle(-sqrt(85)/3,0,0.04),arc(0,0,2sqrt(85)/3,-14/3)

)}}}

Edwin</pre>