write an equation of the circle with center $(9, -8)$ and radius $4$.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Equation of a Circle", "Standard Form of Circle" ], "current_concepts": [ "Equation of a Circle", "Standard Form of Circle" ] } ## Identify the standard equation of a circle $$ (x - h)^2 + (y - k)^2 = r^2 $$ ## Substitute the given center and radius $$ \begin{aligned} &(h, k) = (9, -8) \ &r = 4 \ &(x - 9)^2 + (y - (-8))^2 = 4^2 \end{aligned} $$ ## Simplify the equation $$ (x - 9)^2 + (y + 8)^2 = 16 $$ Write an equation of the circle with center $(9, -8)$ and radius $4$. $(x - 9)^2 + (y + 8)^2 = 16$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Equation of a Circle" ] }

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Question

Explanation:

Identify the standard equation of a circle

Substitute the given center and radius

Simplify the equation

Answer: