question 5 of 10

the circle below is centered at the point (-3, 4) and has a radius of length 3. what is its equation?

a. $(x + 3)^2 + (y - 4)^2 = 9$
b. $(x - 3)^2 + (y + 4)^2 = 9$
c. $(x - 4)^2 + (y + 3)^2 = 3^2$
d. $(x + 4)^2 + (y - 3)^2 = 3^2$

Question

question 5 of 10

the circle below is centered at the point (-3, 4) and has a radius of length 3. what is its equation?

a. $(x + 3)^2 + (y - 4)^2 = 9$
b. $(x - 3)^2 + (y + 4)^2 = 9$
c. $(x - 4)^2 + (y + 3)^2 = 3^2$
d. $(x + 4)^2 + (y - 3)^2 = 3^2$

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" ], "new_concepts": [], "current_concepts": [ "Circle Definition", "Circle Radius" ] } ## Identify the standard equation of a circle $$ (x - h)^2 + (y - k)^2 = r^2 $$ ## Substitute the given center and radius $$ \begin{aligned} &(h, k) = (-3, 4) \ &r = 3 \ &(x - (-3))^2 + (y - 4)^2 = 3^2 \end{aligned} $$ ## Simplify the equation $$ (x + 3)^2 + (y - 4)^2 = 9 $$

(A) $(x + 3)^2 + (y - 4)^2 = 9$

(B) $(x - 3)^2 + (y + 4)^2 = 9$

(C) $(x - 4)^2 + (y + 3)^2 = 3^2$

(D) $(x + 4)^2 + (y - 3)^2 = 3^2$

{ "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

Substitute the given center and radius

Simplify the equation

Answer: