Answer
Fill the blanks with
$y=\displaystyle \frac{3}{2}x$ ... $y=-\displaystyle \frac{3}{2}x$.
Work Step by Step
The hyperbola $\displaystyle \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$
has a horizontal transverse axis and two asymptotes
$y=\displaystyle \frac{b}{a}x$ and $y=-\displaystyle \frac{b}{a}x$.
----------
$\displaystyle \frac{x^{2}}{2^{2}}-\frac{y^{2}}{3^{2}}=1$
$a=2, \quad b=3.$ The asymptotes are
$y=\displaystyle \frac{3}{2}x$ and $y=-\displaystyle \frac{3}{2}x$.
Fill the blanks with
$y=\displaystyle \frac{3}{2}x$ ... $y=-\displaystyle \frac{3}{2}x$.
