Find locus if P(z) is a variable point and `A(z_1)and B(z_2)` are the two fixed points in the argand plane `|z-z_1+|z-z_2|=k`

If P(z) is a variable point and A(z_(1)) and B(z_(2)) are the two fixed points in the argand plane |z-z_(1)|+|z-z_(2)|=k

Results (1) If P(z) is a variable point and A(z_(1)) and B(z_(2)) are the two fixed points in the argand plane; |z-z_(1)|=|z-z_(2)|

If P(z) is a variable point and A(z_(1)) and B(z_(2)) are the two fixed points in the argand plane |z-z_(1)|+|z-z_(2)|=|z_(1)-z_(2)|

If P(z) is a variable point and A(z_(1)) and B(z_(2)) are the two fixed points in the argand plane |z-z_(1)|-|z-z_(2)||=|z_(1)-z_(2)|

If P(z) is a variable point and A(z_(1)) and B(z_(2)) are the two fixed points in the argand plane |z-z_(1)|^(2)+|z-z_(2)|^(2)=|z_(1)-z_(2)|^(2)

If P(z) is a variable point and A(z_(1)) and B(z_(2)) are the two fixed points in the argand plane |z-z_(1)|-|z-z_(2)|-|z_(1)-z_(2)|

If P(z) is a variable point and A(z_(1)) and B(z_(2)) are the two fixed points in the argand plane arg((z-z_(1))/(z-z_(2)))=alpha

If P(z) is a variable point and A(z_(1)) and B(z_(2)) are the two fixed points in the argand plane (i)arg ((z-z_(1))/(z-z_(2)))=+-(pi)/(2) (ii) arg((z-z_(1))/(z-z_(2)))=0 or alpha

If P(z) is a variable point and A(z_(1)) and B(z_(2)) are the two fixed points in the argand plane |z-z_(0)|=|(bar(boldsymbol alpha)z_(0)+alphabar(z)_(0)+r)/(2| alpha|))

If A(z_(1)) and B(z_(2)) are two fixed points in the Argand plane the locus of point P(z) satisfying |z-z_(1)|+|z-z_(2)|=|z_(1)-z_(2)| , is