Sketch a graph of the circle based on the following equation: ${(x-2)}^2+{(y+3)}^2=1$

• A.
• B.
• C.
• D.

Answer: (B)

Verified step by step guidance

1. Step 1: Recognize the equation of the circle in the form (x−h)^2 + (y−k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
2. Step 2: Identify the center of the circle from the equation (x−2)^2 + (y+3)^2 = 1. The center is (h, k) = (2, -3).
3. Step 3: Determine the radius of the circle by taking the square root of the constant on the right-hand side of the equation. Since r^2 = 1, the radius r = √1 = 1.
4. Step 4: Plot the center of the circle at the point (2, -3) on the coordinate plane.
5. Step 5: Draw a circle with radius 1, centered at (2, -3). Ensure the circle extends 1 unit in all directions from the center.