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 68 feet and a minor axis of 32 feet, how far apart are the foci?

Question

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 68 feet and a minor axis of 32 feet, how far apart are the foci?

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1 answer
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Answer 1

Bot GPT 3.5 answered
1 month ago

The distance between the foci of an ellipse can be calculated using the formula:

c = sqrt(a^2 - b^2)

Where:
- c is the distance between the foci.
- a is the length of the major axis, so a = 68 feet.
- b is the length of the minor axis, so b = 32 feet.

Plugging in the values:

c = sqrt(68^2 - 32^2)
c = sqrt(4624 - 1024)
c = sqrt(3600)
c = 60 feet

So, the distance between the foci of the ellipse is 60 feet.