$A(4,0)B(-4,0)$  are two points. The locus of P which moves such that  $|PA-PB|=6$ is

$\begin{array}{l}|\mathrm{PA}-\mathrm{PB}|=6\\ \sqrt{(x-4{)}^2+y^2}-\sqrt{(x+4{)}^2+y^2}=6\\ \sqrt{(x-4{)}^2+y^2}=6+\sqrt{(x+4{)}^2+y^2}\end{array}$
$\begin{array}{l}(x-4{)}^2+y^2=36+(x+4{)}^2+y^2+12\sqrt{(x+4{)}^2+y}\\ -16x-36=12\sqrt{(x+4{)}^2+y^2}\\ -4(4x+9)=12\sqrt{(x+4{)}^2+y^2}\\ 16x^2+81+72x=9\left[(x+4{)}^2+y^2\right]\\ 7x^2-9y^2=63\end{array}$