, , 
 
, so 
 
, so 
 
The center (h,k) = (-2,4)
 
We start out plotting the center C(h,k) = C(-2,4)
 

 
Next we draw the left semi-transverse axis,
which is a segment a=2 units long horizontally 
left from the center.  This semi-transverse
axis ends up at one of the two vertices (-4,4).
We'll call it V1(-4,4):
 

 
Next we draw the right semi-transverse axis,
which is a segment a=5 units long horizontally 
right from the center. This other semi-transverse
axis ends up at the other vertex (0,4).
We'll call it V2(0,4):
 

 
That's the whole transverse ("trans"="across",
"verse"="vertices", the line going across from
one vertex to the other. It is 2a in length,
so the length of the transverse axis is 2a=2(2)=4
 
Next we draw the upper semi-conjugate axis,
which is a segment b=5 units long verically 
upward from the center.  This semi-conjugate
axis ends up at (-2,9).


 

 
Next we draw the lower semi-conjugate axis,
which is a segment b=8 units long verically 
downward from the center.  This semi-conjugate
axis ends up at (-2,-1). 
 


 
That's the complete conjugate axis. It is 2b in length,
so the length of the transverse axis is 2b=2(5)=10
 
Next we draw the defining rectangle which has the
ends of the transverse and conjugate axes as midpoints
of its sides:



 
Next we draw and extend the two diagonals of this defining
rectangle:



Now we can sketch in the hyperbola:


 
Edwin