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 writing down 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 the right side: \(\frac{4x^{2}}{36} - \frac{9y^{2}}{36} = \frac{36}{36}\).
3. Simplify the fractions: \(\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1\).
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. Conclude that since the equation has a subtraction between the squared terms and equals 1, the graph represents a hyperbola.