What are the equations of the asymptotes of the hyperbola $9x^2 - 4y^2 = 36$? A - HSC - SSCE Mathematics Extension 2 - Question 2 - 2018 - Paper 1

From the equation $\frac{x^2}{4} - \frac{y^2}{9} = 1$, we find that:

• $a^2 = 4 \Rightarrow a = 2$
• $b^2 = 9 \Rightarrow b = 3$

The asymptotes of a hyperbola of the form $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ are given by:

$y = \pm \frac{b}{a} x$

Substituting the values of $b$ and $a$:

$y = \pm \frac{3}{2} x$

The equations of the asymptotes are:

$y = \pm \frac{3}{2} x$

Thus, the correct answer is option C: $y = \pm \frac{3}{2} x$.