Question

question 15 of 25

what is the center of the circle given by the equation \\((x - 2)^2 + (y + 4)^2 = 6\\)?

a. \\((-2, -4)\\)
b. \\((2, 4)\\)
c. \\((-2, 4)\\)
d. \\((2, -4)\\)

Explanation:

Identify the standard form of a circle equation

$$ (x - h)^2 + (y - k)^2 = r^2 $$

Compare the given equation to the standard form

$$ (x - 2)^2 + (y + 4)^2 = 6 \implies (x - 2)^2 + (y - (-4))^2 = (\sqrt{6})^2 $$

Extract the coordinates of the center

$$ (h, k) = (2, -4) $$

Answer:

• A. (-2, -4)
• B. (2, 4)
• C. (-2, 4)
• D. (2, -4) (Correct answer)