Graph the following ellipse:
$\frac{y^2}{64}=1-(x+2{)}^2$

• A.
• B.
• C.
• D.

Answer: (A)

Verified step by step guidance

1. Start with the given equation of the ellipse: \(\frac{y^2}{64} = 1 - (x+2)^2\).
2. Rewrite the equation to the standard form of an ellipse by isolating terms: \(\frac{y^2}{64} + (x+2)^2 = 1\).
3. Identify the center of the ellipse from the equation. Since the term is \((x+2)^2\), the center is at \((-2, 0)\).
4. Recognize the denominators to find the lengths of the semi-major and semi-minor axes. Here, \(a^2 = 64\) (vertical axis) and \(b^2 = 1\) (horizontal axis), so \(a = 8\) and \(b = 1\).
5. Plot the ellipse centered at \((-2, 0)\) with vertices at \((-2, 8)\) and \((-2, -8)\) (along the y-axis), and co-vertices at \((-3, 0)\) and \((-1, 0)\) (along the x-axis).