If a pebble is dropped into a pond in the shape of an 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?

Question

ranga · Answer

Distance between foci = $2*\sqrt{a^2-b^2}$
where a is semi-major axis  and  b is semi-minor axis.

tester97 · Answer

thanks ranga so the answer here would be 8? because a^2-b^2=4^2 and the square root of that is just 4 and that times two is 8?

ranga · Answer

a = 20/2 = 10
b = 16/2 = 8
a^2 - b^2 = 10^2 - 8^2 = 100 - 64 = 36
sqrt(a^2-b^2) = sqrt(36) = 6
2*6 = 12

ranga · Answer

"a" is semi-major axis and so you have to divide the length of the major axis by 2.

tester97 · Answer

OHHHHHHHHH I get it now thanks :)

ranga · Answer

You are welcome.