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
(type an ordered pair. simplify your answer.)

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
(type an ordered pair. simplify your answer.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Standard Form of Circle", "Equation of a Circle" ], "new_concepts": [], "current_concepts": [ "Standard Form of Circle", "Equation of a Circle", "Domain and Range of a Circle" ] } ## Identify the center of the circle Using the *Standard Form of Circle* and *Equation of a Circle* knowledge points $$ \begin{aligned} &(x-h)^2 + (y-k)^2 = r^2 \ &(x+4)^2 + (y-6)^2 = 4 \ &h = -4, \quad k = 6 \ &\text{Center: } (-4, 6) \end{aligned} $$ ## Determine the radius of the circle Using the *Standard Form of Circle* and *Equation of a Circle* knowledge points $$ \begin{aligned} &r^2 = 4 \ &r = \sqrt{4} = 2 \end{aligned} $$ ## Find the domain of the circle Using the *Domain and Range of a Circle* knowledge point $$ \begin{aligned} &\text{Domain: } [h - r, h + r] \ &[-4 - 2, -4 + 2] = [-6, -2] \end{aligned} $$ ## Find the range of the circle Using the *Domain and Range of a Circle* knowledge point $$ \begin{aligned} &\text{Range: } [k - r, k + r] \ &[6 - 2, 6 + 2] = [4, 8] \end{aligned} $$ The center is $(-4, 6)$ { "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": 3, "fillColor": "rgba(140, 85, 242, 0.15)", "hasInnerPoints": true } } ], "timestamps": [0.1] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Standard Form of Circle" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the center of the circle

Determine the radius of the circle

Find the domain of the circle

Find the range of the circle

Answer: