Question

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

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

what are the values of (a) and (b)?
a. (a = pm 4) and (b = pm 3)
b. (a = pm 9) and (b = pm 16)
c. (a = pm 3) and (b = pm 4)
d. (a = pm 16) and (b = pm 9)

Explanation:

Step1: Match to hyperbola standard form

The standard vertical hyperbola form is $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$.

Step2: Identify $a^2$ and $b^2$

From $\frac{y^2}{16}-\frac{x^2}{9}=1$, we get $a^2=16$, $b^2=9$.

Step3: Solve for $a$ and $b$

$a=\pm\sqrt{16}=\pm4$, $b=\pm\sqrt{9}=\pm3$

Answer:

A. $a=\pm4$ and $b=\pm3$