this circle is centered at the origin, and the length of its radius is 5. what is the equation of the circle?

a. $\frac{x^2}{5} + \frac{y^2}{5} = 1$
b. $x^2 + y^2 = 5$
c. $x^2 + y^2 = 5^2$

Question

this circle is centered at the origin, and the length of its radius is 5. what is the equation of the circle?

a. $\frac{x^2}{5} + \frac{y^2}{5} = 1$
b. $x^2 + y^2 = 5$
c. $x^2 + y^2 = 5^2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Circle Equation", "Standard Form of Circle" ], "new_concepts": [], "current_concepts": [ "Circle Equation", "Standard Form of Circle" ] } ## Identify the standard form of a circle centered at the origin $$ x^2 + y^2 = r^2 $$ ## Substitute the given radius into the equation $$ \begin{aligned} &r = 5\ &x^2 + y^2 = 5^2 \end{aligned} $$

(A) $\frac{x^2}{5} + \frac{y^2}{5} = 1$

(B) $x^2 + y^2 = 5$

(C) $x^2 + y^2 = 5^2$

{ "elements": [ { "type": "circle", "params": [[0, 0], 5], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "Circle", "withLabel": false } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "O(0,0)", "size": 3, "color": "#583C87", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circle Equation" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the standard form of a circle centered at the origin

Substitute the given radius into the equation

Answer: