If the length of the minor axis of an ellipse is 6 units and the length of the major axis is 10 units, how far from the center are the foci located?

A) 4 units
B) 2 units
C) √4 units
D) √8 units
E) 5 units

a = 5

b = 3
a^2 = b^2 + c^2

so, c = 4

c=4

To find the distance from the center to the foci of an ellipse, we can use the Pythagorean theorem.

The formula to find the distance from the center to the foci of an ellipse is:

c = √(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 length of the semi-major axis (a) is half of the length of the major axis, so a = 10/2 = 5 units. The length of the semi-minor axis (b) is half of the length of the minor axis, so b = 6/2 = 3 units.

Plugging these values into the formula, we get:

c = √(5^2 - 3^2)
c = √(25 - 9)
c = √16
c = 4 units

Therefore, the distance from the center to the foci of the ellipse is 4 units.

Answer: A) 4 units

To find the distance from the center to the foci of an ellipse, we can use the formula:

c = √(a^2 - b^2)

Where "c" represents the distance from the center to each focus, "a" is the length of the semi-major axis, and "b" is the length of the semi-minor axis.

In this case, the length of the major axis is 10 units, so the length of the semi-major axis is 10/2 = 5 units. Similarly, the length of the minor axis is 6 units, so the length of the semi-minor axis is 6/2 = 3 units.

Now we can substitute these values into the formula:

c = √(5^2 - 3^2)
c = √(25 - 9)
c = √16
c = 4 units

Therefore, the distance from the center to the foci is 4 units. Hence, the correct answer is option A) 4 units.