For the hyperbola $9x^2 - 4y^2 =36$, identify the vertices, foci, and asymptotes, then graph

Question

I don't know how to go about this question; an explanation going through the process of finding the vertices, foci, and asymptotes would be helpful.

$9x^{2}-4y^{2}=36$

Answer 1

Rewrite the given equation as :

$$\frac{x^2}{4}-\frac{y^2}{9}=1$$

Now compare the given equation with standard hyperbola : $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$ (Notice $a<b$)

Now,

Foci : $(\pm ae,0)$ ( Here $e$ is the eccenticity of hyperbola, given by $e^2=1+\dfrac{b^2}{a^2}$)

Vertices : $(\pm a,0)$

And the Asymptotes equation is given by : $$y = \pm \frac{b}{a} x$$

You can proceed now.