Question

if a pebble is dropped into a pond in the shape of air ellipse at the location of one focus, the waves will converge at the location of the other focus. If the pond has a major axis of 20 feet and a minor axis of 16 feet, how far apart are the foci

Answer 1

For a given ellipse, there are two foci, each of distance, c, from the centre of the ellipse and the two foci are along the line of the major axis.
The distance of the focus of an ellipse, from the center of the ellipse is given by
$c= \sqrt{a^2-b^2}$
where: a is the length of the major axis and b is the length of the minor axis.

Thus, $c= \sqrt{20^2-16^2} = \sqrt{400-256} = \sqrt{144} =12 \ feet$

Therefore, the distance apart of the two foci is given by
2c = 2(12) = 24 feet.