question 9 of 10

what is the equation of a circle centered at the origin with radius 15?

a. $x^2 + y^2 = 15$
b. $x^3 + y^3 = 15$
c. $x^3 + y^3 = 225$
d. $x^2 + y^2 = 225$

Question

question 9 of 10

what is the equation of a circle centered at the origin with radius 15?

a. $x^2 + y^2 = 15$
b. $x^3 + y^3 = 15$
c. $x^3 + y^3 = 225$
d. $x^2 + y^2 = 225$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Circle Definition", "Circle Radius", "Origin Definition" ], "new_concepts": [], "current_concepts": [ "Circle Definition", "Circle Radius", "Origin Definition" ] } ## State the standard equation of a circle centered at the origin $$ x^2 + y^2 = r^2 $$ ## Substitute the given radius into the equation $$ \begin{aligned} r &= 15 \ r^2 &= 15^2 = 225 \end{aligned} $$ ## Write the final equation $$ x^2 + y^2 = 225 $$

A. $x^2 + y^2 = 15$

B. $x^3 + y^3 = 15$

C. $x^3 + y^3 = 225$

D. $x^2 + y^2 = 225$

{ "elements": [ { "type": "circle", "params": [[0, 0], 6], "properties": { "name": "Circle (r=15)", "strokeColor": "#8C55F2", "strokeWidth": 2, "fillColor": "rgba(140, 85, 242, 0.1)", "withLabel": true } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "Origin (0,0)", "color": "#583C87", "size": 4, "withLabel": true } } ], "timestamps": [0.5] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circle Definition" ] }

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QUESTION IMAGE

Question

Explanation:

State the standard equation of a circle centered at the origin

Substitute the given radius into the equation

Write the final equation

Answer: