The equation \(4x^2 - 9y^2 - 36 = 0\) can be rearranged into a standard form.
First, let's isolate the terms involving \(x\) and \(y\):
\[ 4x^2 - 9y^2 = 36 \]
Next, divide everything by 36 to normalize the equation:
\[ \frac{4x^2}{36} - \frac{9y^2}{36} = 1 \]
Simplifying gives:
\[ \frac{x^2}{9} - \frac{y^2}{4} = 1 \]
This is the standard form of a hyperbola:
\[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \]
where \(a^2 = 9\) (so \(a = 3\)) and \(b^2 = 4\) (so \(b = 2\)).
The graph of this equation will be a hyperbola that opens horizontally.
Given this information, the best choice would be:
- An image shows two curves beside each other opening outward (which represents the hyperbola).
Thus, the correct answer is the image showing two curves beside each other opening outward.