1. **State the problem:** We are given the equation $$16x^2 + y^2 = 16$$ and asked to analyze it. 2. **Identify the type of conic:** This is an ellipse equation in standard form. The general form of an ellipse centered at the origin is $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$. 3. **Rewrite the equation in standard form:** Divide both sides by 16: $$\frac{16x^2}{16} + \frac{y^2}{16} = \frac{16}{16}$$ which simplifies to $$x^2 + \frac{y^2}{16} = 1$$ 4. **Interpret the ellipse parameters:** Here, $$a^2 = 1$$ and $$b^2 = 16$$, so $$a = 1$$ and $$b = 4$$. 5. **Axes lengths:** The ellipse is stretched along the y-axis with semi-major axis length 4 and semi-minor axis length 1 along the x-axis. 6. **Final form:** The ellipse equation is $$\frac{x^2}{1^2} + \frac{y^2}{4^2} = 1$$ This describes an ellipse centered at the origin, wider vertically than horizontally. **Answer:** The equation represents an ellipse centered at the origin with semi-major axis 4 along the y-axis and semi-minor axis 1 along the x-axis.