Tools & Utilitieswy51ai/edulab
edu-analytic-geometry
Turn an analytic geometry problem into a self-contained interactive teaching webpage: left column with problem statement + dynamic console (a variable parameter slider driving real-time recalculation of geometric quantities + theoretical range/fixed value indication), middle column with step-by-step explanations using KaTeX, right column with 2D Canvas dynamic geometry drawing board (ellipse/hyperbola/parabola/circle + moving lines/moving points + vectors + annotations + brush doodling). Supports three entry points—given text problems, random problem generation, and solving problems after uploading and recognizing problem images. Covers problem types such as finding standard equations, chord lengths, vector dot product ranges/fixed values, triangle area maxima/minima, fixed points, fixed values (product of slopes), loci, and eccentricities. Uses a unified method of "setting parametric line x=my+c + simultaneous equations + Vieta's formulas + substitution/constant separation", driven by sympy for precise calculations (answers, coordinates, step values, and theoretical ranges of the interactive engine are consistent from the same source). Other agents can also call this skill to generate such webpages. It parallels edu-solid-geometry in form but uses Canvas-2D + KaTeX (instead of Three.js). Trigger words: 解析几何, 圆锥曲线, 椭圆, 双曲线, 抛物线, 直线与圆锥曲线, 焦点弦, 弦长, 数量积取值范围, 向量数量积, 定点问题, 定值问题, 斜率之积, 三角形面积最值, 轨迹方程, 离心率, 解这道解析几何题, 随机出一道圆锥曲线题, 这张图里的解析几何题; analytic geometry, conic sections, ellipse, hyperbola, parabola, chord length, dot product range, fixed point, fixed value, locus, eccentricity, interactive analytic geometry solution page.