Conic Section Finder

Conic Section Finder is a math puzzle game for students, educators, and anyone who enjoys a clever challenge. Five hidden conic sections — circles, ellipses, parabolas, and hyperbolas — are lurking somewhere on a Cartesian coordinate grid. Your job is to find them all.

How it works

You can't see the curves directly. Instead, you probe the grid by firing horizontal or vertical lines at it: type x=3 or y=-2 and the game reveals exactly where your line intersects each hidden curve. The intersection points are marked with distinct colored symbols — each conic gets its own color and shape so you can track them independently. From those intersection coordinates, you reason out the equation of each curve and type it in.

The challenge

Intersections alone don't give you the equation for free. A single point on a circle tells you almost nothing — but four or five intersections, carefully placed, let you triangulate the center and radius. Parabolas and hyperbolas take a different kind of thinking. You'll need to reason about symmetry, vertex location, and the shape of each curve to nail down the right equation. The fewer shots you fire before solving all five, the better your score.

Features

• Six conic section types: circles, ellipses, upward/downward parabolas, left/right parabolas, horizontal hyperbolas, and vertical hyperbolas
• All coefficients are whole numbers, so no decimal-hunting
• Distinct color + symbol for every curve — circle ●, ellipse ◆, parabola ▲ ▶, hyperbola ■ ✚
• Shot history log showing every intersection point you've found
• Hint system that reveals a center, vertex, or key parameter when you're stuck
• Give Up reveals all five curves drawn on the grid with their equations
• High score tracking (fewest shots to solve all five) persists across sessions
• Fullscreen, single HTML file — works in any modern browser, no installation

Who is this for?

This game works well as a study tool for precalculus or algebra II students learning conic sections for the first time, as a warmup exercise for math teachers, or as a straightforward logic puzzle for anyone comfortable with coordinate geometry. The equation format cheat sheet is always visible on screen, so you don't need to have the standard forms memorized to play.