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

\x^2 + (y - 5)^2 = 16\

what is the center of the circle?

the circle is centered at the point (0,5)
(type an ordered pair.)

what is the radius of the circle?

the radius of the circle is
(type an integer or a fraction.)

Question

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

\x^2 + (y - 5)^2 = 16\

what is the center of the circle?

the circle is centered at the point (0,5)
(type an ordered pair.)

what is the radius of the circle?

the radius of the circle is
(type an integer or a fraction.)

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 standard form parameters Using the *Standard Form of Circle* and *Equation of a Circle* knowledge points $$ \begin{aligned} &(x-h)^2 + (y-k)^2 = r^2 \ &x^2 + (y-5)^2 = 16 \ &h = 0, \quad k = 5, \quad r^2 = 16 \end{aligned} $$ ## Determine center and radius Using the *Equation of a Circle* knowledge point $$ \begin{aligned} &\text{Center: } (h, k) = (0, 5) \ &\text{Radius: } r = \sqrt{16} = 4 \end{aligned} $$ The radius of the circle is 4 { "elements": [ { "type": "point", "params": [[0, 5]], "properties": { "name": "Center (0,5)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "circle", "params": [[0, 5], 4], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "fillColor": "rgba(140, 85, 242, 0.15)", "hasInnerPoints": true } } ], "timestamps": [0.5] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Equation of a Circle" ] }

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Question

Explanation:

Identify standard form parameters

Determine center and radius

Answer: