Question

if the point (x,y) is equidistant from the point (10,0)(0,-10) and(-8,6),then prove that x=0,y=0

Answer 1

(10-x)^2+y^2=x^2+(y+10)^2
x+y=0

(x+8)^2+(y-6)^2=(x-10)^2+(y)^2
16x-12y=-20x
3x+y=0

solving x=0, y=0