Question

guided practice
fill in the table with the information needed to graph the equation (9y^2 - 16x^2 = 144).
144.

equation of hyperbola	standard form of the equation	transverse axis	values of (a) and (b)	vertices	dimensions of central rectangle

hyperbolas
what is the height and the width of the central rectangle?
a. height = 9 and width = 16
b. height = 4 and width = 3
c. height = 3 and width = 4
d. height = 8 and width = 6

Explanation:

Step1: Recall rectangle dimensions rule

For hyperbola $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$, height=$2a$, width=$2b$

Step2: Identify $a$ and $b$ values

Given $a=4$, $b=3$

Step3: Calculate height

$\text{height}=2a=2\times4=8$

Step4: Calculate width

$\text{width}=2b=2\times3=6$

Answer:

D. height = 8 and width = 6