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? (1 point)
A. 30
B. 35
C. 54
D. 60
The distance between the foci of an ellipse can be found using the formula:
c = sqrt(a^2 - b^2)
Where a is the length of the semi-major axis and b is the length of the semi-minor axis.
In this case, the major axis is 68 feet, so the semi-major axis (a) is half of that, which is 34 feet. The minor axis is 32 feet, so the semi-minor axis (b) is half of that, which is 16 feet.
Now, we can calculate the distance between the foci:
c = sqrt(34^2 - 16^2)
c = sqrt(1156 - 256)
c = sqrt(900)
c = 30
Therefore, the distance between the foci is 30 feet.
Answer: A. 30