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

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

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Standard Form of Circle", "Equation of a Circle", "Domain and Range of a Circle", "Interval Notation" ], "new_concepts": [], "current_concepts": [ "Standard Form of Circle", "Equation of a Circle", "Domain and Range of a Circle", "Interval Notation" ] } ## Identify the center and radius Using the *Standard Form of Circle* and *Equation of a Circle* knowledge points $$ \begin{aligned} &(x-h)^2 + (y-k)^2 = r^2 \ &(x+4)^2 + (y-6)^2 = 4 \ &h = -4, \quad k = 6, \quad r^2 = 4 \implies r = 2 \ &\text{Center: } (-4, 6), \quad \text{Radius: } 2 \end{aligned} $$ ## Determine the domain Using the *Domain and Range of a Circle* and *Interval Notation* knowledge points $$ \begin{aligned} &\text{Domain: } [h - r, h + r] \ &[-4 - 2, -4 + 2] = [-6, -2] \end{aligned} $$ ## Determine the range Using the *Domain and Range of a Circle* and *Interval Notation* knowledge points $$ \begin{aligned} &\text{Range: } [k - r, k + r] \ &[6 - 2, 6 + 2] = [4, 8] \end{aligned} $$ ## Question 1 The center is $(-4,6)$ ## Question 2 The radius is 2 ## Question 3 Express the domain of the relation in interval notation $[-6,-2]$ ## Question 4 Express the range of the relation in interval notation $[4,8]$ { "elements": [ { "type": "point", "params": [[-4, 6]], "properties": { "name": "Center (-4,6)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "circle", "params": [[-4, 6], 2], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "fillColor": "rgba(140, 85, 242, 0.15)", "hasInnerPoints": true } } ], "timestamps": [0.5] } { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Equation of a Circle" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the center and radius

Determine the domain

Determine the range

Answer:

Question 1

Question 2

Question 3

Question 4