Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the domain and range.

\\((x + 4)^2 + (y - 6)^2 = 4\\)

the center is \\((-4, 6)\\)
(type an ordered pair. simplify your answer.)

the radius is \\(2\\)
(type an integer or a simplified fraction.)

graph the circle.

express the domain of the relation in interval notation.

Explanation:

Identify the center and radius

Using the Standard Form of Circle and Equation of a Circle knowledge points

$$
LATEXBLOCK0
$$

Determine the domain of the circle

Using the Domain and Range of a Circle and Interval Notation knowledge points

$$
LATEXBLOCK1
$$

Determine the range of the circle

Using the Domain and Range of a Circle and Interval Notation knowledge points

$$
LATEXBLOCK2
$$

Answer:

Question 1

The center is \((-4, 6)\).

Question 2

The radius is \(2\).

Question 3

The domain of the relation in interval notation is \([-6, -2]\).

Question 4

The range of the relation in interval notation is \([4, 8]\).