Identify whether the equation is of an ellipse or hyperbola.
$\frac{x^2}{16}+\frac{y^2}{9}=1$

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

Answer: (A)

Verified step by step guidance

1. Look at the given equation: \(\frac{x^2}{16} + \frac{y^2}{9} = 1\).
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 terms are added and positive; a hyperbola has the form \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) or \(-\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), where one term is subtracted.
3. Notice that in the given equation, the \(x^2\) and \(y^2\) terms are added together, and both denominators (16 and 9) are positive.
4. Since the equation matches the form of an ellipse (sum of two squared terms equal to 1), it represents an ellipse.
5. Therefore, identify the conic as an ellipse based on the structure of the equation.