Problem Analysis #39

Kimi K3 · Run 1

Correct
5.34s
469 toks

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 24 Consider the parabola y2 = 12(x−2). Find the distance between its focus and its directrix. [3 points] ①6 ②7 ③8 ④9 ⑤10

Ground Truth
①
Recorded model response / solution
Reasoning Process

The parabola y2=12(x−2)y^2 = 12(x-2) is in the form y2=4p(x−h)y^2 = 4p(x-h) with vertex (2,0)(2,0).

Since 4p=124p = 12, we get p=3p = 3.

  • Focus: (2+p,0)=(5,0)(2+p, 0) = (5, 0)
  • Directrix: x=2−p=−1x = 2-p = -1

The distance between the focus and the directrix is 2p=62p = 6.

\boxed{①}

Final Model Output
①

Comparative Analysis (P39) (Average across runs)

Averages use reported measurements only. Missing usage is not treated as zero.

Avg Time Taken

Kimi K3
1934.3
Solar Pro 4
13.2
Motif 3
11.7
K-EXAONE-2
0.8

Avg Token Usage

Solar Pro 4
613.3
Kimi K3
454.0
K-EXAONE-2
332.3
    CSAT 2026 · Problem 39 · Kimi K3 | EntropyMath