Question

If point $(x,y)$ is equidistant from point $(3,k)$ and $(k,3)$ then find the value of $k$ when $x\ne y$

Answer 1

if (x,y)is equidistant form point (3,k)& (k,3).

then

$\sqrt{(x-3{)}^2+(y-k{)}^2=(x-k{)}^2+(y-3{)}^2}$

on both sides=

$(x-3{)}^2+(y-k{)}^2=(x-k{)}^2+(y-3{)}^2$

$x^2+9-6x+y^2+k^2-2ky=y^2+x^2-2kx+9+6y+k^2$

(2k-6)x=(2k-6)y

(2k-6)(x-y)=0[x+y]then

then 2k-6=0

[k=3]