SOLUTION: The vertices of a hyperbola are the points (−3, 2) and (−3, −2) and the length of its conjugate is 6. Find the equation of the hyperbola, the coordinates of its foci, and it

From the given info, the center of the hyperbola is the point (-3,0)

and its real axis lies on vertical line x = -3.


    Thus the hyperbola is "vertical", opened up and down.  


Real semi-axis length is half the distance between the vertices  a =  =  = 2.


Also, from the given part, the length of its conjugate axis is 6; hence, conjugate semi-axis length is  b = 6/2 = 3.


Now the standard form equation of the hyperbola is

     -  = 1.    ANSWER


                            P L O T


    


                 Hyperbola  -  = 1



In the plot, we can not see the imaginary axis and imaginary semi-axes: they are invisible.  

But we can show the foci.  They are  (,)  and  (,),  where 13 =  +  =  + .