Indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola.
$4x^2-9y^2=36$

• A. A circle
• B. An ellipse
• C. A hyperbola
• D. A parabola

Answer: (C)

Verified step by step guidance

1. Start by examining the given equation: \$4x^2 - 9y^2 = 36$.
2. Rewrite the equation in standard form by dividing every term by 36 to isolate 1 on one side: \(\frac{4x^2}{36} - \frac{9y^2}{36} = \frac{36}{36}\).
3. Simplify the fractions to get: \(\frac{x^2}{9} - \frac{y^2}{4} = 1\).
4. Recognize the form of the equation: it matches the standard form of a hyperbola, which is \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) or \(\frac{y^2}{b^2} - \frac{x^2}{a^2} = 1\).
5. Since the equation has a subtraction between the squared terms and equals 1, this confirms the graph is a hyperbola.