1. ## Hyperbola question

My teacher said this was badly worded but I still want to solve it:

"Two megaphones shaped like trumpets are attached to the roof of a car, sending sound waves in both directions. These megaphonees were designed to follow a hyperbola with vertices at (0, 8) and (0, -8), and foci at (0, 10) and (0, -10) in a Cartesian plane. The total length of the megaphones is 96cm. What is the diameter of the trumpets?"

Any help would be greatly appreciated!

2. Originally Posted by s3a
My teacher said this was badly worded but I still want to solve it:

"Two megaphones shaped like trumpets are attached to the roof of a car, sending sound waves in both directions. These megaphonees were designed to follow a hyperbola with vertices at (0, 8) and (0, -8), and foci at (0, 10) and (0, -10) in a Cartesian plane. The total length of the megaphones is 96cm. What is the diameter of the trumpets?"

You can write that hyperbola as $\frac{y^2}{64}- \frac{x^2}{b^2}= 1$. Further, the information about the foci tells you that $64+ b^2= 100$ so $b^2= 36$.
The equation of the hyperbola is $\frac{y^2}{64}- \frac{x^2}{36}= 1$. The radius of the trumpets is the y value when x= 96.