The equation visible in the image is:

$4x^2 + 9y^2 - 36 = 0$

This is the equation of an ellipse in standard form. To rewrite it in a clearer format, we can divide the entire equation by 36 to simplify it:

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

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

This is the standard form of an ellipse equation: $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ Where $a^2 = 9$ and $b^2 = 4$, meaning that $a = 3$ and $b = 2$.

Thus, the ellipse has:

• Semi-major axis $a = 3$
• Semi-minor axis $b = 2$
• The center of the ellipse is at $(0, 0)$, since there are no terms involving $x$ or $y$ shifts.

Let me know if you would like further details on ellipses or how to graph this equation.

Here are five related questions to explore further:

1. How do you find the foci of an ellipse?
2. What happens if the signs of $x^2$ and $y^2$ are different in the ellipse equation?
3. How can the equation of a circle be derived from the equation of an ellipse?
4. How does changing the coefficients of $x^2$ and $y^2$ affect the shape of the ellipse?
5. What are the standard forms of hyperbola equations, and how do they differ from ellipses?

Tip: Always divide through by the constant term in the equation when simplifying conic sections like ellipses or hyperbolas to easily compare it to the standard form.