locus of z such that `|z-a|^2+|z-b|^2=lambda` is real is

The locus of z such that |z-1|^2+|z+1|^2=4 is a

The locus of z such that (z^(2))/(z-1) is always real is

The locus of z such that (z^(2))/(z-1) is always real is

The locus of complex number z such that z is purely real and real part is equal to - 2 is

Let z_1=3 and z_2=7 represent two points A and B respectively on complex plane . Let the curve C_1 be the locus of pint P(z) satisfying |z-z_1|^2 + |z-z_2|^2 =10 and the curve C_2 be the locus of point P(z) satisfying |z-z_1|^2 + |z-z_2|^2 =16 The locus of point from which tangents drawn to C_1 and C_2 are perpendicular , is :

Let z_1=3 and z_2=7 represent two points A and B respectively on complex plane . Let the curve C_1 be the locus of pint P(z) satisfying |z-z_1|^2 + |z-z_2|^2 =10 and the curve C_2 be the locus of point P(z) satisfying |z-z_1|^2 + |z-z_2|^2 =16 The locus of point from which tangents drawn to C_1 and C_2 are perpendicular , is :

Let Z_(1),Z_(2) be two complex numbers which satisfy |z-i| = 2 and |(z-lambda i)/(z+lambda i)|=1 where lambda in R, then |z_(1)-z_(2)| is

If |z+i|^2-|z-i|^2=3 then the locus of z is

If a is real number such that |z-ai|=|z+ai| , then the locus of z is

Statement - 1 : If for any complex number z, |z-2|+|z-3|=4 , then are bounded by the locus of z is 3pi sq. units. Statement -2 : If |z-a| + |z-b|= |b-a| , then locus of z will be line segment joining a and b.