Question 888991
your equation is as follows:


(x+4)^2/4 + (y-6)^2/36 = 1


the graph of your equation is shown below:


look below the graph for further comments.


<img src = "http://theo.x10hosting.com/2014/072806.jpg" alt="$$$" </>


the length of your vertical axis is equal to (11 - (-1)) = 12.
the length of your horizontal axis is equal to (-6 - (-2) = 4.


the general form of the equation of an ellipse is:


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


a is half the length of the horizontal axis which is equal to 2 which makes a^2 = 4.


b is half the length of the vertical axis which is equal to 6 which makes b^2 = 36


c is the distance between the focal points.


the formula for c is:


c^2 = |a^2 - b^2|


the absolute value sign is necessary because c is always positive and sometimes a is bigger than b (horizontal major axis) and sometimes b is bigger than a (vertical major axis.


your c^2 is equal to |4-25| which is equal to 21 which makes c equal to sqrt(21).


your focal points will be along the major axis at (-4,6-sqrt(21)) and (-4,6+sqrt(21)).


on the graph these focal points show up at (-4,0.417) and (-4,9.583).


the center of your graph is midway between the  vertices which puts it at (-4,5).