write the standard form of the equation of the circle with its center at $(-4, 0)$, and a radius of 6.

what is the equation of the circle in standard form?

(simplify your answer)

Question

write the standard form of the equation of the circle with its center at $(-4, 0)$, and a radius of 6.

what is the equation of the circle in standard form?

(simplify your answer)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "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 of a circle $$ (x - h)^2 + (y - k)^2 = r^2 $$ ## Substitute the given center and radius $$ \begin{aligned} (h, k) &= (-4, 0) \ r &= 6 \ (x - (-4))^2 + (y - 0)^2 &= 6^2 \end{aligned} $$ ## Simplify the equation $$ (x + 4)^2 + y^2 = 36 $$ What is the equation of the circle in standard form? $(x + 4)^2 + y^2 = 36$ (Simplify your answer) { "elements": [ { "type": "point", "params": [[-4, 0]], "properties": { "name": "Center (-4, 0)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "circle", "params": [[-4, 0], 6], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2, "fillColor": "rgba(85, 131, 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 of a circle

Substitute the given center and radius

Simplify the equation

Answer: