Question

question 4 of 10

the circle below is centered at the point (1, 2) and has a radius of length 3.
what is its equation?

a. \\((x - 2)^2 + (y - 1)^2 = 3^2\\)
b. \\((x - 2)^2 + (y + 1)^2 = 9\\)
c. \\((x - 1)^2 + (y + 2)^2 = 9\\)
d. \\((x - 1)^2 + (y - 2)^2 = 3^2\\)

Explanation:

Identify the standard equation of a circle

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

Substitute the given center and radius

$$
LATEXBLOCK0
$$

Match with the given options

$$ (x - 1)^2 + (y - 2)^2 = 3^2 \implies \text{Option D} $$

Answer:

• A. \((x - 2)^2 + (y - 1)^2 = 3^2\)
• B. \((x - 2)^2 + (y + 1)^2 = 9\)
• C. \((x - 1)^2 + (y + 2)^2 = 9\)
• D. \((x - 1)^2 + (y - 2)^2 = 3^2\) (Correct answer)