Question 1030970
Let (x,y) be a point on the curve.

Then {{{sqrt((x+4)^2 + y^2) - sqrt((x-4)^2 + y^2) = 2}}}

==> {{{sqrt((x+4)^2 + y^2) = sqrt((x-4)^2 + y^2) + 2}}}

==> {{{(x+4)^2 + y^2 = (x-4)^2 + y^2 + 4sqrt((x-4)^2 + y^2) +4}}}, after squaring both sides...

==> {{{4x - 1 = sqrt((x-4)^2 + y^2)}}}, after reducing further..

==> {{{16x^2 - 8x +1 = x^2 - 8x+16 +y^2}}} after squaring both sides.

==> {{{15x^2 - y^2 = 15}}}

==> {{{x^2 - y^2/15 = 1}}}, which is a hyperbola center at (0,0) and x-axis as transverse axis.