The center of the circle is at (−1, 1).
What is the equation of the circle?
A. (x – 1)² + (y + 1)² = 8
B. (x + 1)² + (y – 1)² = 8
C. (x – 1)² + (y + 1)² = 16
D. (x + 1)² + (y – 1)² = 16
The center of the circle is at (−1, 1). What is the equation of the circle?
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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).