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` (fixed), then find locus of z.

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

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)|=|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)|-|z-z_(2)||=|z_(1)-z_(2)|

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 (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_(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_(0)|=|(bar(boldsymbol alpha)z_(0)+alphabar(z)_(0)+r)/(2| alpha|))

Let A(z_(1)),B(z_(2)) are two points in the argand plane such that (z_(1))/(z_(2))+(bar(z)_(1))/(bar(z)_(2))=2. Find the value of