Write the standard form equation of each ellipse centered at the origin.

• A. $\frac{x^2}{4}+y^2=1$
• B. $x^2+\frac{y^2}{16}=1$
• C. $x^2+y^2=16$
• D. $\frac{x^2}{16}+y^2=1$

Answer: (D)

Verified step by step guidance

1. Identify the center of the ellipse. Since the ellipse is centered at the origin, the center is at (0, 0).
2. Determine the lengths of the major and minor axes by observing the ellipse on the coordinate grid. The ellipse extends from -4 to 4 along the x-axis, so the length of the major axis is 8, and the semi-major axis length is 4.
3. Observe the ellipse's extent along the y-axis. It extends from -1 to 1, so the length of the minor axis is 2, and the semi-minor axis length is 1.
4. Write the standard form equation of the ellipse centered at the origin, which is given by \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), where \(a\) is the semi-major axis and \(b\) is the semi-minor axis.
5. Substitute the values of \(a = 4\) and \(b = 1\) into the equation to get \(\frac{x^2}{16} + \frac{y^2}{1} = 1\).