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 examining the given equation: \(y^2 - \frac{x^2}{16} = 1\).
2. Recall the general forms of conic sections: an ellipse typically 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. Notice that in the given equation, the \(y^2\) term is positive and the \(x^2\) term is subtracted, matching the form of a hyperbola.
4. Since the equation fits the hyperbola form, it represents a hyperbola rather than an ellipse.
5. Therefore, identify the conic as a hyperbola based on the presence of subtraction between the squared terms.