Question

Find the set of points the difference of the squares of whose distances from two given points A and B is constant.

Answer 1

let the two points be $A=(a,b)$ and $B=(p,q)$. Let the given constant be $k$.

Then the locus of the point is given by

$(x-a{)}^2+(y-b{)}^2-(x-p{)}^2-(y-q{)}^2=k$

$⟹2(p-a)x+2(q-b)y+a^2+b^2-p^{-}{q}^2-k=0$