Graph the following ellipse:
$\frac{x^2}{36}=1-y^2$

• A.
• B.
• C.
• D.

Answer: (B)

Verified step by step guidance

1. Start with the given equation of the ellipse: \(\frac{x^2}{36} = 1 - y^2\).
2. Rewrite the equation to isolate terms on one side: \(\frac{x^2}{36} + y^2 = 1\).
3. Recognize this as the standard form of an ellipse centered at the origin: \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), where \(a^2 = 36\) and \(b^2 = 1\).
4. Identify the lengths of the semi-major and semi-minor axes: \(a = 6\) and \(b = 1\).
5. Plot the ellipse centered at the origin with vertices at \((\pm 6, 0)\) and co-vertices at \((0, \pm 1)\).