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 standard 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, while 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, both \(\frac{x^2}{16}\) and \(\frac{y^2}{9}\) are positive and added together, matching the form of an ellipse.
4. Confirm that the right side of the equation is 1, which is consistent with the standard form of an ellipse or hyperbola.
5. Conclude that since the equation matches the form \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) with positive terms, the graph represents an ellipse.