Identify whether the equation is of an ellipse or hyperbola.
$y^2-\frac{x^2}{16}=1$

• A. Ellipse
• B. Hyperbola
• C. Neither of the above

Answer: (B)

Verified step by step guidance

1. Start by writing down the given equation: \(y^{2} - \frac{x^{2}}{16} = 1\).
2. Recall the general forms of conic sections: an ellipse has the form \(\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1\), where both squared terms are added, and a hyperbola has the form \(\frac{y^{2}}{a^{2}} - \frac{x^{2}}{b^{2}} = 1\) or \(\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1\), where one squared term is subtracted from the other.
3. Compare the given equation to these forms. Notice that the equation has a subtraction between the squared terms: \(y^{2} - \frac{x^{2}}{16} = 1\).
4. Since the equation matches the form of a hyperbola (one squared term minus another equals 1), identify the conic as a hyperbola.
5. Conclude that the equation represents a hyperbola because of the subtraction between the squared terms and the equal sign to 1.