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? 8.5 focus 18 focus a. 8.5 b. 26.5 c. 9.5 d. 10.5

Explanation:

Step1: Recall ellipse property

The sum of the distances from any point on the ellipse to the two foci is equal to the length of the major - axis. Let the length of the red line segment be $a = 8.5$, the distance between the foci be $d=18$, and the length of the blue line segment be $x$.

Step2: Set up equation

According to the ellipse property, $a + x$ is equal to the semi - major axis length times 2. Since the sum of the distances from a point on the ellipse to the two foci is constant, we have $a+x=\text{major - axis length}$. And for an ellipse, if the distance between the foci is $d$ and the lengths of the line - segments from a point on the ellipse to the foci are $a$ and $x$, we know that $a + x$ is a constant. Here, $a+x$ is the semi - major axis length times 2. The sum of the distances from a point on the ellipse to the two foci is constant. So $x=18 + 8.5-8.5=10.5$.

Answer:

D. 10.5