Chapter 10.2, Problem 64PE

A returning boomerang is a V-shaped throwing device made from two wings that are set at a slight tilt and that have an airfoil design. One side is rounded and the other side is flat,similar to an airplane propeller. When thrown properly, a boomerang follows a circular flight path and should theoretically return close to the point of release.

The boomerang pictured is approximately in the shape of one branch of a hyperbola (although the two wings are in slightly different planes). To construct the hyperbola, an engineer needs to know the location of the foci.

Determine the location of the focus to the right of the center if the vertex is $7.5\text{ in}$ . from the center and the equations of the asymptotes are $y=\pm \frac{4}{5}x$ Round the coordinates to the nearest tenth of an inch.