Answer
The thumbtacks: $(±\sqrt 5,0)~ft$
The length of the string $=2\sqrt 5~ft$
Work Step by Step
The major axis is horizontal.
The major axis is equal to the width of 6 feet:
$2a=6$
$a=3$
The half of the minor axis is equal to the height of 2 feet:
$b=2$
$a^2=b^2+c^2$
$c^2=a^2-b^2=3^2-2^2=5$
$c=\sqrt 5$
The thumbtacks must be placed at the foci. When major axis is horizontal:
$(±c,0)=(±\sqrt 5,0)$
The length of the string is equal to $2c=2\sqrt 5$
