The equation of a circle is (x+2)^(2)+(y+6)^(2)=16. What are the center and radius of the circle? Choose 1 answer: (A) The center is (2,-6) and the radius is 6 . (B) The center is (-2,6) and the radius is 6 . (c) The center is (-2,-6) and the radius is 4 . (D) The center is (1,2) and the radius is 16 .

Circle Equation Form: The general form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.Compare Given Equation: Compare the given equation (x+2)² + (y+6)² = 16 with the general form to find the center (h, k) and the radius r.Find Center and Radius: The given equation can be rewritten as (x - (-2))² + (y - (-6))² = 16, which shows that h = -2 and k = -6. Therefore, the center of the circle is (-2, -6).Calculate Radius: To find the radius r, we look at the right side of the equation, which is 16. Since the general form is r², we take the square root of 16 to find r. The square root of 16 is 4, so the radius is 4.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The equation of a circle is
(x+2)^(2)+(y+6)^(2)=16. What are the center and radius of the circle?
Choose 1 answer:
(A) The center is
(2,-6) and the radius is 6 .
(B) The center is
(-2,6) and the radius is 6 .
(c) The center is
(-2,-6) and the radius is 4 .
(D) The center is
(1,2) and the radius is 16 .

The equation of a circle is $(x+2)^{2}+(y+6)^{2}=16$ . What are the center and radius of the circle? $\newline$ Choose $1$ answer: $\newline$ (A) The center is $(2,-6)$ and the radius is $6$ . $\newline$ (B) The center is $(-2,6)$ and the radius is $6$ . $\newline$ (C) The center is $(-2,-6)$ and the radius is $4$ . $\newline$ (D) The center is $(1,2)$ and the radius is $16$ .

View step-by-step help

Home

Math Problems

Algebra 1

Compare linear and exponential growth

Full solution

Q. The equation of a circle is

(x+2)^{2}+(y+6)^{2}=16

. What are the center and radius of the circle?

\newline

Choose

1

answer:

\newline

(A) The center is

(2,-6)

and the radius is

6

\newline

(B) The center is

(-2,6)

and the radius is

6

\newline

(-2,-6)

and the radius is

4

\newline

(D) The center is

(1,2)

and the radius is

16

Circle Equation Form: The general form of the equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$ , where $(h, k)$ is the center of the circle and $r$ is the radius.
Compare Given Equation: Compare the given equation $x+2)^2 + (y+6)^2 = 16\ with the general form to find the center \$h, k$ and the radius $r$ .
Find Center and Radius: The given equation can be rewritten as $x - (-2))^{2} + (y - (-6))^{2} = 16\, which shows that \$h = -2$ and $k = -6$ . Therefore, the center of the circle is $(-2, -6)$ .
Calculate Radius: To find the radius $r$ , we look at the right side of the equation, which is $16$ . Since the general form is $r^2$ , we take the square root of $16$ to find $r$ . The square root of $16$ is $4$ , so the radius is $4$ .