To determine the length of the major axis of an ellipse, we need to understand a fundamental property of ellipses: the sum of the distances from any point on the ellipse to the two foci is always constant and equal to the length of the major axis.
Let’s denote the distances from a point on the ellipse to the two foci as follows:
- Distance to the first focus: 11 units
- Distance to the second focus: 7 units
According to the ellipse's property, the length of the major axis (denoted as [tex]\( 2a \)[/tex]) is given by the sum of these two distances:
[tex]\[ 2a = \text{distance to the first focus} + \text{distance to the second focus} \][/tex]
Substituting the given values, we get:
[tex]\[ 2a = 11 + 7 \][/tex]
[tex]\[ 2a = 18 \][/tex]
Therefore, the length of the major axis of the ellipse is 18 units.
To sum up, we know that the length of the major axis is 18 units because, by the fundamental property of ellipses, the sum of the distances from any given point on the ellipse to its two foci is equal to the length of the major axis. In this case, adding the two given distances (11 units and 7 units) confirms that the major axis is 18 units long.
