Hello, rtblue!
Horace is an avid fisherman whose favorite fishing spot is a perfectly elliptical pond
with a maximum width of 144 meters and a maximum length of 240 meters.
Horace has found the best spots for fishing in this pond are at the foci of the pond.
So one day he sets off from the bank of the pond and rows directly to the closest focus.
Finding no fish at this spot, he rows to the second focus, only to discover he has left
the rest of his bait back on the bank at his original starting point on the bank.
He rows back to the original starting point to pick up his bait.
How many meters has Horace rowed?
We are expected to know the geometric characteristics of an ellipse.
Center this ellipse at the origin.
We have: .$\displaystyle a = 120,\:b = 72$
The foci are: .$\displaystyle c^2 \:=\:a^2b^2 \:=\:120^272^2 \:=\:9216 \quad\Rightarrow\quad c \:=\:\pm 96$
Code:
72♥
 P
 o(x,y)
 * *
* *
*  *
*  *
F2 *  *F1
 ♥   o       +       o   ♥  
120 96  96 120




72♥

Horace rowed from $\displaystyle \,P$ to $\displaystyle F_1$, then $\displaystyle F_1$ to $\displaystyle F_2$, then $\displaystyle F_2$ back to $\displaystyle \,P.$
We know that $\displaystyle \overline{F_1F_2} = 192.$
What about $\displaystyle \overline{PF_1} + \overline{PF_2}$ ?
Given any point $\displaystyle \,P$ on an ellipse, the sum of the distances from $\displaystyle \,P$
. . to the two foci is a constant, namely, $\displaystyle 2a.$
. . That is: .$\displaystyle \overline{PF_1} + \overline{PF_2} \:=\:2(120) \:=\:240$
Therefore, he rowed: .$\displaystyle 192 + 240 \:=\:432\text{ meters.}$