Question

Show that the path of a moving point which remains at equal distance from the points $(2,1)$ and $(-3,-2)$ is a straight line.

Answer 1

It is very well known that locus of point which is equidistant from the two given point is the perpendicular bisector of line joining those points .

It can be easily shown by making distance of point (say (h,k)) equal from the two given points i.e

$(h-2{)}^2+(k-1{)}^2=(h+3{)}^2+(k+2{)}^2$

which gives $5h+3k+4=0$