Question

Homing pigeons avoid flying over large bodies of​ water, preferring to fly around them instead. Assume that a pigeon released from a boat
6
6
miles
miles from the shore of a lake​ (point B in the​ figure) flies first to point P on the shore and then along the straight edge of the lake to reach its home at L. If L is
12
12 miles from point​ A, the point on the shore closest to the​ boat, and if a pigeon needs
four thirds
4
3
as much energy per mile to fly over water as over​ land, find the location of point​ P, which minimizes energy used.

Answer 1

Fix your post, typing in a normal way, and describe the diagram which we obviously cannot see

Answer 2

If we let x = the distance AP, then the energy used is
z = 4/3 √(x^2+6^2) + 12-x
dz/dx = 4x/(3√(x^2+36)) - 1
so find where dz/dx=0