Question

If two points (2, 3) and (-6, -5) are equidistant from the point (x, y), show that x + y + 3 = 0.

Answer 1

$A(2,3)$ & $B(-6,-5)$ are equidistance from $C(x,y)$

$AC=BC$

$\sqrt{(x-2{)}^2+(y-3{)}^2}=\sqrt{(x+6{)}^2+(y+5{)}^2}$

$x^2+4-4x+y^2+9-6y$

$=x^2+36+12x+y^2+25+10y$

$16x+16y+48=0$

$x+y+3=0$

Hence proved