Question

question 2 of 25

what is the equation of a circle with center (-4, 7) and radius 6?

a. \\((x + 4)^2 + (y - 7)^2 = 36\\)
b. \\((x + 4)^2 + (y - 7)^2 = 6\\)
c. \\((x - 4)^2 + (y + 7)^2 = 6\\)
d. \\((x - 4)^2 + (y + 7)^2 = 36\\)

Explanation:

Identify standard form parameters

$$ (h, k) = (-4, 7),\quad r = 6 $$

Substitute into standard equation

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

$$ (x - (-4))^2 + (y - 7)^2 = 6^2 $$

Simplify the equation

$$ (x + 4)^2 + (y - 7)^2 = 36 $$

Answer:

• A. \((x + 4)^2 + (y - 7)^2 = 36\) (Correct answer)
• B. \((x + 4)^2 + (y - 7)^2 = 6\)
• C. \((x - 4)^2 + (y + 7)^2 = 6\)
• D. \((x - 4)^2 + (y + 7)^2 = 36\)