Find the equation of a hyperbola whose foci are  and which pass through point (2, 3).

The foci of the hyperbola are  which lie on y-axis.
∴ The standard equation of the hyperbola is                                                   ...(i)
It passes through (2, 3)                                                                            ...(ii)
The foci are 
But,                             ...(iii)
Using (iii) in (ii), we have 
        
           
When  from (iii),   (not possible)
When 
∴                          
Hence, from (i), the equation of the hyperbola is:  or