Question

question 3 of 10

the circle below is centered at the point \\((5, 3)\\) and has a radius of length 4.
what is its equation?

a. \\((x + 5)^2 + (y + 3)^2 = 16\\)
b. \\((x - 3)^2 + (y - 5)^2 = 16\\)
c. \\((x + 3)^2 + (y + 5)^2 = 16\\)
d. \\((x - 5)^2 + (y - 3)^2 = 16\\)

Explanation:

Identify the standard equation of a circle

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

Substitute the given center and radius

$$
LATEXBLOCK0
$$

Simplify the equation

$$ (x - 5)^2 + (y - 3)^2 = 16 $$

Answer:

• A. \((x + 5)^2 + (y + 3)^2 = 16\)
• B. \((x - 3)^2 + (y - 5)^2 = 16\)
• C. \((x + 3)^2 + (y + 5)^2 = 16\)
• D. \((x - 5)^2 + (y - 3)^2 = 16\) (Correct answer)