question 5 of 10

the length of the red line segment is 8, and the length of the blue line segment is 3. how long is the major axis of the ellipse?

a. 5

b. 11

c. 24

d. 8

Question

question 5 of 10

the length of the red line segment is 8, and the length of the blue line segment is 3. how long is the major axis of the ellipse?

a. 5

b. 11

c. 24

d. 8

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Ellipse Definition" ], "new_concepts": [], "current_concepts": [ "Ellipse Definition", "Ellipse Foci" ] } ## Identify the given values and geometric properties $$ \begin{aligned} &d_1 = 8 \quad \text{(distance from a point on the ellipse to the first focus)} \ &d_2 = 3 \quad \text{(distance from the same point to the second focus)} \end{aligned} $$ ## Apply the definition of an ellipse $$ \begin{aligned} &d_1 + d_2 = 2a \ &2a = \text{length of the major axis} \end{aligned} $$ ## Calculate the major axis length $$ \begin{aligned} &2a = 8 + 3 \ &2a = 11 \end{aligned} $$

A. 5

B. 11

C. 24

D. 8

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

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QUESTION IMAGE

Question

Explanation:

Identify the given values and geometric properties

Apply the definition of an ellipse

Calculate the major axis length

Answer: