If the points `(2,\ 1)` and `(1,\ -2)` are equidistant from the point `(x ,\ y)` , show that `x+3y=0` .

If the point P(x ,\ y) is equidistant from the points A(5,\ 1) and B(1,\ 5) , prove that x=y .

Show that the points (1, 1, 1) and (-3, 0, 1) are equidistant from the plane 3x+4y-12 z+13=0.

If the point (x , y) is equidistant from the points (a+b , b-a) and (a-b , a+b) , prove that b x=a y

If the point (x, y) is equidistant from the points (2, 3) and (6, -1) , find the relation between x and y .

Point P(x,y) is equidistant from the points A(-2,0) and B(3,-4) Prove that : 10 x - 8 y = 21.

Show that the point (2,2) is equidistant from the point (-1,-2) and (-3,2) .

Find the point on y-axis which is equidistant from the points (3,1,2) and (5,5,3),

If the point P(x, y) be equidistant from the points (a+b, b-a) and (a-b, a + b) , prove that (a-b)/(a+b) = (x-y)/(x+y) .

Find the point on y-axis which is equidistant from the ponts (5,5,2) and (3,1,2) .

Find the locus of a point equidistant from the point (2,4) and the y-axis.