Question

center: ( , ) radius: r = equation: ² + ² = ² answer choices (x - 1) (x + 1) (y - 1) (x - 2) (x + 2) (y + 1) (x + 3) (y - 2) (y + 2) 1 -1 x (y - 3) 2 -2 y 3 -3 0

Explanation:

Step1: Find the center coordinates

Looking at the graph, the center of the circle is at (2, 3) because it's 2 units to the right of the origin on the x - axis and 3 units up on the y - axis.

Step2: Find the radius

The radius is the distance from the center to the edge of the circle. From the center (2, 3), moving 1 unit (since the circle spans 1 unit in radius on the grid), so \(r = 1\).

Step3: Write the circle equation

The standard equation of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius. Substituting \(h = 2\), \(k = 3\), and \(r = 1\), we get \((x - 2)^2+(y - 3)^2=1^2\) or \((x - 2)^2+(y - 3)^2 = 1\).

Answer:

Center: \((2,3)\)
Radius: \(r = 1\)
Equation: \((x - 2)^2+(y - 3)^2=1\)