Question

question 8 of 10
the length of the transverse axis is 11, and the length of the red line segment is 19. how long is the blue line segment?
a. 11
b. 19
c. 30
d. 8

Explanation:

Step1: Recall hyperbola property

For a hyperbola, the difference of the distances from any point on the hyperbola to the two foci is equal to the length of the transverse axis. Let the length of the blue - line segment be $x$, the length of the red line segment be $r = 19$, and the length of the transverse axis be $t=11$. Then $|r - x|=t$.

Step2: Solve for $x$

We have two cases: $r - x=t$ or $x - r=t$. If $r - x=t$, then $19 - x = 11$, and $x=19 - 11=8$. If $x - r=t$, then $x=19 + 11 = 30$. But in the context of the hyperbola's distance - difference property, we take the positive difference such that $|r - x|=t$. Since $r>t$, we have $x=r - t$.

Answer:

D. 8