question 10 of 10

which is the standard equation for a circle centered at the origin with radius $r$?

a. $x^2 + y^2 = r$

b. $x + y = r$

c. $x^2 = y^2 + r^2$

d. $x^2 + y^2 = r^2$

Question

question 10 of 10

which is the standard equation for a circle centered at the origin with radius $r$?

a. $x^2 + y^2 = r$

b. $x + y = r$

c. $x^2 = y^2 + r^2$

d. $x^2 + y^2 = r^2$

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" ] } ## Recall the standard equation of a circle $$ (x - h)^2 + (y - k)^2 = r^2 $$ ## Substitute the given center and radius $$ \begin{aligned} (h, k) &= (0, 0) \ (x - 0)^2 + (y - 0)^2 &= r^2 \ x^2 + y^2 &= r^2 \end{aligned} $$

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

B. $x + y = r$

C. $x^2 = y^2 + r^2$

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

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

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QUESTION IMAGE

Question

Explanation:

Recall the standard equation of a circle

Substitute the given center and radius

Answer: