If an elliptic race track is 100 yards long and 20 yards wide, then how far apart are the foci?
To find the distance between the foci of an elliptical race track, we need to know the dimensions of the major and minor axes of the ellipse. The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter that intersects the major axis at a right angle.
In this case, you mentioned that the race track is 100 yards long and 20 yards wide. Assuming that the long side of the oval shape represents the major axis, and the short side represents the minor axis, we now have the required information to calculate the distance between the foci.
The formula to find the distance between the foci of an ellipse can be given as:
Distance between Foci = 2 * √(a² - b²)
Where 'a' represents the semi-major axis (half the length of the major axis), and 'b' represents the semi-minor axis (half the length of the minor axis).
Given that the length of the race track is 100 yards (which represents the major axis), the semi-major axis (a) would be half of that, which is 50 yards.
And given that the width of the race track is 20 yards (which represents the minor axis), the semi-minor axis (b) would be half of that, which is 10 yards.
Now, we can substitute the values into the formula:
Distance between Foci = 2 * √(50² - 10²)
Simplifying further:
Distance between Foci = 2 * √(2500 - 100)
Distance between Foci = 2 * √2400
Using a calculator, we can calculate the square root of 2400, which equals approximately 48.99.
Therefore, the distance between the foci of the given elliptic race track is approximately 48.99 yards.
Place your ellipse into standard position,
a = 50, b = 10
for such as ellipse:
c^2 + b^2 = a^2
find c,
the distance between 2 foci would be 2c