Question

Find the locus of the point such that the difference of its distances from the points (0, -6) and (0, 6) is 3 units.

Answer 1

Let O be $(0,-6)$ and P be $(0,6)$ .Consider OP is the distance between $O$ and $P$

$\sqrt{(x-0{)}^2+(y+6{)}^2}=\sqrt{(x-0{)}^2+(y-6{)}^2}=3\Rightarrow x^2+y^2+12y+36=x^2+y^2-12y+36=3\Rightarrow 24y=3\therefore y=\frac{1}{8}$