circles in the coordinate plane

which of the following is the graph of
$(x - 3)^2 + (y + 1)^2 = 9$?

Question

circles in the coordinate plane

which of the following is the graph of
$(x - 3)^2 + (y + 1)^2 = 9$?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Circle Equation", "Graphing Circles" ], "new_concepts": [], "current_concepts": [ "Circle Equation", "Graphing Circles" ] } ## Identify center and radius Using the *Circle Equation* knowledge point $$ \begin{aligned} &(x-h)^2 + (y-k)^2 = r^2\ &(x-3)^2 + (y+1)^2 = 9\ &h = 3,\quad k = -1 \implies \text{Center: } (3, -1)\ &r^2 = 9 \implies r = 3 \end{aligned} $$ ## Analyze the given graphs Using the *Graphing Circles* knowledge point $$ \begin{aligned} &\text{First graph: Center is at } (3, 1), \text{ radius is } 3.\ &\text{Second graph: Center is at } (3, -1), \text{ radius is } 3.\ &\text{Third graph: Center is at } (-3, -1), \text{ radius is } 3. \end{aligned} $$

(A) Circle with center (3, 1) and radius 3

(B) Circle with center (3, -1) and radius 3

(C) Circle with center (-3, -1) and radius 3

{ "elements": [ { "type": "point", "params": [[3, -1]], "properties": { "name": "Center (3, -1)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "circle", "params": [[3, -1], 3], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "fillColor": "rgba(140, 85, 242, 0.15)" } } ], "timestamps": [0.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Graphing Circles" ] }

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QUESTION IMAGE

Question

Explanation:

Identify center and radius

Analyze the given graphs

Answer: