The equation given is:

$4x^2 + 9y^2 = 36$

To determine the type of conic section, let's rewrite the equation in a more standard form.

First, divide both sides of the equation by 36 to normalize the equation:

$\frac{4x^2}{36} + \frac{9y^2}{36} = \frac{36}{36}$

Simplify each term:

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

This is the standard form of the equation for an ellipse:

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

where $a^2 = 9$ and $b^2 = 4$.

Thus, the given equation represents an ellipse.

Would you like more details or have any questions about this solution?

Here are 5 related questions you might find helpful:

1. How do you determine the foci of an ellipse?
2. What is the standard form of a hyperbola?
3. How can you identify a parabola from its equation?
4. What are the major and minor axes of an ellipse?
5. How do you find the eccentricity of an ellipse?

Tip: When identifying conic sections, always try to rewrite the equation in its standard form. This will help you recognize the type of conic section more easily.