The given equation is:

$\frac{1}{9}y^2 - \frac{1}{100}x^2 = 1$

This is the equation of a hyperbola in standard form, which can be written as:

$\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$

By comparing this equation with the given one, we can identify the values of $a^2$ and $b^2$:

$\frac{y^2}{3^2} - \frac{x^2}{10^2} = 1$

Thus, we have:

• $a^2 = 9$, so $a = 3$,
• $b^2 = 100$, so $b = 10$.

Finding the vertices:

For a hyperbola of the form $\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$, the transverse axis is along the $y$-axis. The vertices are located at $y = \pm a$, which means:

$\text{Vertices} = (0, \pm 3)$

Thus, the vertices of the hyperbola are: $(0, 3) \quad \text{and} \quad (0, -3)$

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you find the foci of this hyperbola?
2. What is the equation of the asymptotes for this hyperbola?
3. How would the equation change if the transverse axis was along the $x$-axis?
4. Can you explain the difference between the transverse and conjugate axes in a hyperbola?
5. How would you graph this hyperbola?

Tip: When working with hyperbolas, always check whether the transverse axis is along the $x$-axis or $y$-axis by looking at which term is positive.