Question

the black figure is an ellipse, and the black line segment is its major axis. what is the length of the blue line segment? a 9.5 b. 10.5 c. 26.5 d 8.5

Explanation:

Step1: Recall the property of an ellipse

The sum of the distances from any point on the ellipse to the two foci is equal to the length of the major axis.

Step2: Calculate the length of the blue line segment

Let the length of the blue line segment be \(x\). We know that \(8.5 + x=19\) (since the distance between the two foci is \(18\), and the sum of distances from a point on ellipse to foci is major - axis length. Here, assume major - axis length \(= 19\) (by property). Solving for \(x\): \(x = 19 - 8.5=10.5\)

Answer:

B. 10.5