Question

question 9 of 10 the length of the major axis of the ellipse below is 12, and the length of the red line segment is 4. how long is the blue line segment? focus focus a. 6 b. 8 c. 10 d. 16

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 blue line segment be $x$ and the length of the red line segment be $y = 4$, and the length of the major - axis be $2a=12$.

Step2: Set up equation

We know that $x + y=2a$.
Substitute $y = 4$ and $2a = 12$ into the equation: $x+4 = 12$.

Step3: Solve for $x$

Subtract 4 from both sides of the equation: $x=12 - 4$.
$x = 8$.

Answer:

B. 8