Elementary Curves
Ellipse, circle, hyperbola, parabola, parallel, intersecting and coincident lines. Explore the simplest curves (straight lines) and second degree conics curves.
Elementary Curves
The simplest of all curves are the straight lines. The next in complexity are the second degree or conics curves.
Non-degenerate Conics
Ellipse
x² / a² + y² / b² = 1
where a, b = intrinsic parameters
Circle
x² + y² = a²
where a = radius
Hyperbola
x² / a² - y² / b² = 1
where a, b = intrinsic parameters
Parabola
y² - 2ly = 0
where l = intrinsic parameter
Degenerate Conics
Parallel Lines
x² - a² = 0
where a = half the distance between the parallel lines
Intersecting Lines
x² / a² - y² / b² = 0
where tan⁻¹(b/a) = half the angle between the intersecting lines
Coincident Lines
x² = 0