Question

Find the equation of locus of a point which is equidistant from the point $A(-3,2)$ and $B(0,4)$ ?

Answer 1

Let the point be $(h,k)$.
Given:
$\text{Distance of point from A=Distance of point from B}$
$⟹\sqrt{(h+3{)}^2+(k-2{)}^2}=\sqrt{h^2+(k-4{)}^2}$
$⟹(h+3{)}^2+(k-2{)}^2=h^2+(k-4{)}^2$
$⟹h^2+6h+9+k^2-4k+4=h^2+k^2-8k+16$
$⟹6h-4k+13=-8k+16$
$⟹6h+4k=3$
Replacing $h$ with $x$ and $k$ with $y$:
$6x+4y=3$