Question 860236
The question is most comfortably answered using knowledge of standard form for a hyperbola.


The subtraction is on the {{{y^2}}} term, as indicated by the line containing the vertices.


Center is (2,-3).
{{{a=(6-(-2))/2=4}}}.
c is how far from center to the focus; 
{{{c=2-(-4)=6}}}.
The way that a, b, and c are related is {{{a^2+b^2=c^2}}}.
{{{b^2=c^2-a^2}}}
{{{b^2=36-16}}}
{{{b^2=20}}}, to be used just as that.


Fill the numeric information into standard form.
{{{highlight((x-2)^2/16-(y+3)^2/20=1)}}}


Check your textbook for discussion about the details; or also check the article, <a href="http://en.wikipedia.org/wiki/Hyperbola">http://en.wikipedia.org/wiki/Hyperbola</a>