Crazy Curves — Boom Bunny Studios

Welcome to Crazy Curves

2–4 players take turns drawing a quadratic curve: Ax² + Bxy + Cy² + Dx + Ey + F = 0.
You have 60 seconds to submit numbers for A, B, C, D, E, F.
Your curve appears in light grey first. If it doesn't touch any earlier curve and its visible length ≥ 1, it turns to your color and you score 1 point.
If it intersects any earlier curve or is too short, it vanishes and scores 0.
A round ends when everyone misses in a row. The game ends after each player has started a round.

We'll also explain your curve in kid-friendly terms: its type (circle, ellipse, parabola, hyperbola), where it sits, and where its foci live!

The general quadratic (conic) equation is:

Ax² + Bxy + Cy² + Dx + Ey + F = 0

Δ = B² − 4AC

Ellipse: (x−h)²/a² + (y−k)²/b² = 1
Circle:  (x−h)² + (y−k)² = r²

h, k: Center of the ellipse/circle.
a, b: Semi-axes lengths (a = semi-major, b = semi-minor). For a circle a = b = r.
r: Radius (special case when a = b).
Foci (ellipse): Along the longer axis at distance c where c² = a² − b².
Major axis: The longer diameter (length 2a). Minor axis length 2b.

Vertical:   (x−h)² = 4p(y−k)
Horizontal: (y−k)² = 4p(x−h)

Horizontal: (x−h)²/a² − (y−k)²/b² = 1
Vertical:   (y−k)²/a² − (x−h)²/b² = 1

h, k: Center.
a: Distance from center to each vertex on the transverse axis.
b: Conjugate semi-axis; shapes the asymptote slopes.
c: Focal distance with c² = a² + b²; foci lie along the transverse axis at (h ± c, k) or (h, k ± c).
Vertices: (h ± a, k) or (h, k ± a) depending on orientation.
Asymptotes: y − k = ±(b/a)(x − h) (horizontal) or y − k = ±(a/b)(x − h) (vertical).

If B ≠ 0, rotate axes to remove the xy term before fitting one of these forms.