To find the distance between the foci of an ellipse, we first need to understand the relationship between the axes and the foci in an ellipse. The formula for calculating the distance between the foci is given by:
c = √(a² – b²)
In this formula, c represents the distance from the center of the ellipse to each focus, a is half of the length of the major axis, and b is half of the length of the minor axis.
Given that the major axis is 10 feet, we can calculate:
- a = 10/2 = 5 feet
For the minor axis, which is 6 feet, we have:
- b = 6/2 = 3 feet
Now we can substitute these values into the formula:
c = √(5² – 3²)
This simplifies to:
c = √(25 – 9) = √16 = 4
The total distance between the two foci is then 2c:
Distance between foci = 2 * 4 = 8 feet
In conclusion, the distance between the foci of the ellipse with a major axis of 10 feet and a minor axis of 6 feet is 8 feet.