question 10 of 10

the length of the red line segment is 15, and the length of the blue line segment is 8. how long is the transverse axis?

a. 23
b. 8
c. 7
d. 15

Question

question 10 of 10

the length of the red line segment is 15, and the length of the blue line segment is 8. how long is the transverse axis?

a. 23
b. 8
c. 7
d. 15

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Hyperbola Definition", "Hyperbola Axes" ], "new_concepts": [], "current_concepts": [ "Hyperbola Definition", "Hyperbola Axes", "Transverse Axis" ] } ## Identify the given geometric components and definitions $$ \begin{aligned} &d_1 = 15 \quad (\text{distance from point on hyperbola to far focus}) \ &d_2 = 8 \quad (\text{distance from point on hyperbola to near focus}) \ &|d_1 - d_2| = 2a \quad (\text{definition of a hyperbola}) \ &\text{Transverse Axis Length} = 2a \end{aligned} $$ ## Calculate the length of the transverse axis $$ \begin{aligned} &2a = 15 - 8 \ &2a = 7 \end{aligned} $$

(A) 23

(B) 8

(C) 7

(D) 15

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

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Question

Explanation:

Identify the given geometric components and definitions

Calculate the length of the transverse axis

Answer: