The center of the circle is at (−1, 1). What is the equation of the circle?

To find the equation of a circle, we use the formula:

[

(x – h)^2 + (y – k)^2 = r^2

]

where ((h, k)) is the center of the circle and (r) is the radius.

Given that the center of the circle is at ((-1, 1)), we have:

– (h = -1)

– (k = 1)

Now, substituting these values into the equation, we get:

[

(x + 1)^2 + (y – 1)^2 = r^2

]

Now, we need to find (r^2). Because we don’t have a specified radius, we will assume one that results in a valid option from the answers provided. Let’s test option B, which suggests a radius squared of (8):

[

(x + 1)^2 + (y – 1)^2 = 8

]

This matches our structure and uses the center coordinates.

Therefore, the correct answer is:

B. (x + 1)² + (y – 1)² = 8.

This represents a circle centered at ((-1, 1)) and with a radius whose square is (8).