Sketch a graph of the circle based on the following equation: $x^2+{(y-1)}^2=9$

• A.
• B.
• C.
• D.

Answer: (D)

Verified step by step guidance

1. Identify the standard form of a circle's equation: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
2. Compare the given equation x^2 + (y - 1)^2 = 9 with the standard form to determine the center and radius.
3. From the equation, observe that (h, k) = (0, 1) and r^2 = 9, so the radius r = 3.
4. Plot the center of the circle at the point (0, 1) on the coordinate plane.
5. Draw a circle with a radius of 3 units around the center (0, 1), ensuring it extends 3 units in all directions from the center.