question 3 of 10

this circle is centered at the origin, and the length of its radius is 4. what is the circles equation?

a. $x + y = 4$
b. $x^2 + y^2 = 4$
c. $x^6 + y^6 = 4$
d. $x^2 + y^2 = 16$

Question

question 3 of 10

this circle is centered at the origin, and the length of its radius is 4. what is the circles equation?

a. $x + y = 4$
b. $x^2 + y^2 = 4$
c. $x^6 + y^6 = 4$
d. $x^2 + y^2 = 16$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circle Definition", "Circle Radius", "Origin Definition" ], "new_concepts": [], "current_concepts": [ "Circle Definition", "Circle Radius", "Origin Definition" ] } ## Identify the standard equation of a circle centered at the origin $$ x^2 + y^2 = r^2 $$ ## Substitute the given radius value $$ \begin{aligned} r &= 4 \ r^2 &= 4^2 = 16 \end{aligned} $$ ## Write the final equation $$ x^2 + y^2 = 16 $$

(A) $x + y = 4$

(B) $x^2 + y^2 = 4$

(C) $x^6 + y^6 = 4$

(D) $x^2 + y^2 = 16$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circle Definition" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the standard equation of a circle centered at the origin

Substitute the given radius value

Write the final equation

Answer: