Question 1186881
<pre>
Instead of doing yours for you, I'll do one exactly like yours step by step, so
you can use it as a model to do yours by.  Here is the problem I will do.
Just use your numbers instead of the ones here:

What is the equation of the ellipse having major axis of length 16, center at
(-3,-8), and a focus at (4,-8)?

{{{drawing(500,4500/11,-12,6,-18,4,grid(1),
green(line(-11,-8,5,-8),line(-3,-8+sqrt(15),-3,-8-sqrt(15))),
graph(500,4500/11,-12,6,-18,4), circle(-3,-8,.08),circle(4,-8,.08), arc(-3,-8,16,2sqrt(15)) )}}}

The equation of an ellipse with major axis horizontal is

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

where the center is (h,k) = (-3,-8), and where "a" = semi-major axis length.
The major axis is 16, so the semi-major axis = 8. So far we have

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

{{{(x+3)^2/64}}}{{{""+""}}}{{{(y+8)^2/b^2}}}{{{""=""}}}{{{1}}}

We need "b", which is the semi-minor axis length.  We have to use the
Pythagorean theorem relationship for all ellipses, which is

{{{c^2}}}{{{""=""}}}{{{a^2}}}{{{""-""}}}{{{b^2}}}

where c = distance from center to a focus.  The distance from the center (-3,-8)
to the focus, which is (4,-8) is 7 units, found by counting units on the graph
above.  So b = 7, and the complete equation of the ellipse is

{{{(x+3)^2/64}}}{{{""+""}}}{{{(y+8)^2/7^2}}}{{{""=""}}}{{{1}}}

{{{(x+3)^2/36}}}{{{""+""}}}{{{(y+8)^2/49}}}{{{""=""}}}{{{1}}}

Now do yours exactly, step by step, like this one.

Edwin</pre>