if z is a complex number then |z-3|+|z+3|=10 represents: a circle an ellipse a hyperbola none of the above Share with your friends Share 2 Aarushi Mishra answered this We knowz1-z2 is actually the distance between z1 and z2 on argand planeSoz-3 is distance of z from 3,0 on argand plane and z+3=z--3 is distance of z from -3,0 on argand plane Givenz-3+z+3=10Sum of distances of z from 3,0 and -3,0 is constant=10By definition it should be ellipseThe locus of a point such that sum of distances of it from two fixed point is an ellipseNote: For ellipse we have an additional condition, that sum of distances from two fixed point must be greater than distance between the fixed pointsSum of distances of z from 3,0 and -3,0=10Distance between 3,0 and -3,0=3--32+02=62=6Hence this condition is satisfiedIt is an ellipse 0 View Full Answer