Question

find the relation between x and y, such that the point (x,y) is equidistant from points (-1,8) and (3,4)

Answer 1

The locus is the perpendicular bisector of segment joining the given points.

Midpoint is: (-1+3/2, (8+4)/2)

that is, the bisector passes through (1,6).

Slope is: [(8-4)/(-1-3)]^(-1)×(-1)=1.

Hence required locus (line) is:

y–6=1(x–(1))

y=x+5