Suppose two circles, whose centers are at least 2a units apart (see figure), are centered at F

Question:

Suppose two circles, whose centers are at least 2a units apart (see figure), are centered at F₁ and F₂, respectively. The radius of one circle is 2a + r and the radius of the other circle is r, where r ≥ 0. Show that as r increases, the intersection point P of the two circles describes one branch of a hyperbola with foci at F₁ and F₂.

Нуperbola 2a + r F,