Verify that the locus of a point which moves so that the difference of its distances from points A (4, 0) and B (– 4, 0) is always equal to 2, is a hyperbola in the standard form 

Let the point be .
The fixed points are A (4, 0), B (-4, 0). The given condition is :
                           PA - PB = 2
       
Squaring both sides, we get
                   
                              
Squaring again, we get
                        
Hence, the locus of point P is 
which is the standard form of hyperbola in the form .