write the standard form of the equation of the circle with the given center and radius.

center $(6,4)$, $r = 7$

type the standard form of the equation of the circle.

(simplify your answer.)

Question

write the standard form of the equation of the circle with the given center and radius.

center $(6,4)$, $r = 7$

type the standard form of the equation of the circle.

(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" ] } ## Identify the standard form equation Using the *Standard Form of Circle* and *Equation of a Circle* knowledge points $$ (x - h)^2 + (y - k)^2 = r^2 $$ ## Substitute the given values Using the *Standard Form of Circle* and *Equation of a Circle* knowledge points $$ \begin{aligned} &(h, k) = (6, 4) \ &r = 7 \ &(x - 6)^2 + (y - 4)^2 = 7^2 \end{aligned} $$ ## Simplify the equation Using the *Standard Form of Circle* and *Equation of a Circle* knowledge points $$ (x - 6)^2 + (y - 4)^2 = 49 $$ Type the standard form of the equation of the circle. $(x - 6)^2 + (y - 4)^2 = 49$ (Simplify your answer.) { "elements": [ { "type": "point", "params": [[6, 4]], "properties": { "name": "Center (6,4)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "circle", "params": [[6, 4], 7], "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", "Standard Form of Circle" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the standard form equation

Substitute the given values

Simplify the equation

Answer: