Question

Find the equation of locus of point P, if the point A(1,2), B(3,4) are at equal distance from P

Answer 1

$AP=BP$
$\sqrt{(x-1{)}^2+(y-2{)}^2}=\sqrt{(x-3{)}^2+(y-y{)}^2}$ square
$(x-1{)}^2+(y-2{)}^2=(x-3{)}^2+(y-2{)}^2$
$x^2-2x+1+y^2-4y+y=x^2-6x+9+y^2-4y+y$
$4x=9-1$
$4x=8$
$x=2$ line