API · no tools. This is the prompt and response recorded for this attempt; a full solution may not have been returned.
Problem Statement
This is a Korean CSAT mathematics multiple-choice problem. Solve it and put only the correct choice symbol, one of ①, ②, ③, ④, ⑤, inside \boxed{}.
Problem 26 Letabe a positive real number, and consider the hyperbola x2 a2 − y2 a2 =−1, whose foci areFandF ′. LetPbe the point where the tangent to this hyperbola at (a, √ 2a) meets they-axis. Suppose that P F× P F ′ = 8. Find the value ofa. [3 points] 17 ① √ 3 ② 4 √ 3 3 ③ 5 √ 3 3 ④2 √ 3 ⑤ 7 √ 3 3
Ground Truth
②
Recorded model response / solution
Reasoning Process
\boxed{②}
Final Model Output
②
Comparative Analysis (P41) (Average across runs)
Averages use reported measurements only. Missing usage is not treated as zero.
Avg Time Taken
Motif 3
40.7
Kimi K3
21.8
Solar Pro 4
16.7
K-EXAONE-2
2.5
Avg Token Usage
Solar Pro 4
1153.0
Kimi K3
1091.7
K-EXAONE-2
1071.3