Question

guided practice 144. fill in the table with the information needed to graph the equation $9y^2 - 16x^2 = 144$ what are the equations of the asymptotes? a. $y = \pm \frac{4}{3}x$ b. $y = \pm \frac{3}{4}x$ c. $y = \pm \frac{16}{9}x$ d. $y = \pm \frac{9}{16}x$

Explanation:

Step1: Recall hyperbola asymptote formula

For vertical transverse axis hyperbola $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$, asymptotes are $y=\pm\frac{a}{b}x$

Step2: Identify $a$ and $b$ values

From the table: $a=4$, $b=3$

Step3: Substitute into asymptote formula

$y=\pm\frac{4}{3}x$

Answer:

A. $y = \pm \frac{4}{3}x$