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 isolate terms and put it in the standard form of an ellipse. Add \((x+2)^2\) to both sides to get \(\frac{y^2}{64} + (x+2)^2 = 1\).
3. Recognize that this is the equation of an ellipse centered at \((-2, 0)\), where \(\frac{y^2}{64}\) corresponds to the vertical axis and \((x+2)^2\) corresponds to the horizontal axis.
4. Identify the lengths of the semi-major and semi-minor axes: \(a^2 = 64\) so \(a = 8\) (vertical radius), and \(b^2 = 1\) so \(b = 1\) (horizontal radius).
5. Plot the ellipse centered at \((-2, 0)\) with vertices at \((-2, 8)\) and \((-2, -8)\) (vertical direction), and co-vertices at \((-3, 0)\) and \((-1, 0)\) (horizontal direction).